<figure><img src="image_23.png" /></figure>

# Micromechanical Modeling of high temperature dependent thermo-elastic

## Communication Info

**Authors:**

Nada TASSI ¹,²

Lahcen AZRAR ²

Nadia FAKRI ³

¹ Private University of Marrakech, Marrakech, Morocco

² ENSAM, UM5, Rabat, Morocco

³ FST, Tangier, Morocco

**Keywords:**

(1) Mathematical modeling

(2) Integral equations

(3) Temperature dependent behavior

(4) Effective properties

(5) Green's functions

(6) Micromechanical method

Abdoun, F., & Azrar, L. (2020). Thermal buckling and vibration of laminated

## Abstract

In this paper, the micromechanical modeling of the effective high temperature-dependent behavior of thermo-elastic composite materials is analyzed. The modeling is based on the micro-to-macro transition inclusion problem, employing temperature-dependent localization tensors.

Green's tensors are developed to derive temperature dependent integral equations related to Eshelby's tensors and micromechanical approaches. The effective behavior at high temperatures is determined using micromechanical methods and is presented for various inclusion volume fractions, shapes, and types of reinforced composites.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Farah Abdoun, Lahcen Azrar, Thermal buckling and vibration of laminated composite plates with temperature dependent properties by an asymptotic numerical method, International Journal for Computational Methods in Engineering Science and Mechanics, 2020, 43–57.

[2] Abdoun, F., Azrar, L. Nonlinear thermal analysis of multilayered composite and FGM plates with temperature-dependent properties based on an asymptotic numerical method, 2021, 4361–4387.

[3] A.R. Sánchez-Majano, R. Masia, A. Pagani, E. Carrera, Microscale thermo-elastic analysis of composite materials by high-order geometrically accurate finite elements, Composite Structures, 2022, 300, 116105.

[4] Chen, Y., Shi, X., Zhao, Z. et al. A thermo-viscoelastic model for particle-reinforced composites based on micromechanical modeling. Acta Mech. Sin. 37, 2021, 402–413.
The new fractional calculus and its applications

**Communication Info**

**Authors:**

Abdessamad AIT BRAHIM¹

¹ AMSC Laboratory, University of Sciences and Technology, Beni Mellal, Morocco

**Keywords:**

(1) Conformable fractional derivative

(2) non-conformable fractional derivative

(3) Caputo fractional derivative

**Abstract**

This study presents a comparative analysis of non-conformable and conformable fractional derivatives, alongside the Riemann-Liouville and Caputo fractional derivatives. It evaluates their effectiveness in solving fractional ordinary differential equations and explores their applications in physics through numerical simulations. The results indicate that the conformable fractional derivative shows potential as a viable alternative to the non-conformable, Riemann-Liouville, and Caputo fractional derivatives in the order range of $1/2 < \alpha < 1$.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Ait Brahim, A. El Hajaji, K. Hilal, J. El Ghordaf "On a novel fractional calculus and its applications to well-known problems" European journal of pure and applied mathematics, april 2024. https://doi.org/10.29020/nybg.ejpam.v17i2.5159.

[2] Abdeljawad, T., Baleanub, D. (2017). Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel. Journal of Nonlinear Sciences and Applications (JNSA), 10(3), https://doi.org:10.22436/jnsa.010.03.20.

[3] Atangana, A. (2016). On the new fractional derivative and application to nonlinear Fisher's reaction diffusion equation. Applied Mathematics and computation, https://doi.org/10.1016/j.amc.2015.10.021.

[4] A. Ait Brahim, J. El Ghordaf, A. El Hajaji, K. Hilal, J. E.N.'{a}poles Valdes "A Comparative Analysis of Conformable, Non-conformable, Riemann-Liouville, and Caputo Fractional Derivatives" European journal of pure and applied mathematics, july 2024, doi: https://doi.org/10.29020/nybg.ejpam.v17i2.5159.
<figure><img src="image_24.png" /></figure>

Regional Optimal Control Problem of RiemannLiouville Time
Fractional Bilinear Systems with Bounded Control Operator in a
Finite Time Horizon

**Communication Info**

**Authors:**

Hajar Oukassou
Rachid Larhrissi

MACS Laboratory, Faculty of
Sciences, Moulay Ismail
University, Morocco;
ha.oukassou@edu.umi.ac.ma
r.larhrissi@umi.ac.ma

**Keywords:**

(1) Quadratic cost

(2) Fractional bilinear systems

(3) Optimal control

(4) Regional controllability

**Abstract**

The main goal of this paper is to study the regional optimal control problem with a fixed desired state for a quadratic cost function. In the case of a bounded set of admissible controls, we will characterize the optimal control either for exactly or approximately attainable states. This problem can be formulated as an optimization problem with constraint on the desired state, which can also be approximated by a set of problems without constraint on the desired state.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Zhou, Y., Jiao, F. (2010), Existence of mild solutions for fractional neutral evolution equations. Computers and Mathematics with Applications, 59(3), 1063-107.

[2] Bahaa, G. M. (2016), Fractional optimal control problem for differential system with control constraints.; Filomat, 30(8), 2177-2189.

[3] Gisèle. M. Mophou, Optimal control of fractional diffusion equation; Computers and Mathematics with Applications 61 (2011) 68-78.

[4] Ouhafsa, M., Aadi, A. A. (2023), On the Optimal Control Problem for Bilinear Systems with Bounded and Unbounded Controls.

[5] A. A. AADI AND E. ZERRIK, Regional optimal control of a bilinear plate equation; In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT).
Solving Fractional Integral Equations via
Proinov's Fixed Point Theorem

Communication Info

Authors:

Maha Belhadj¹

¹ Sousse university, Higher
School of sciences and
technologies of H. Sousse,
Tunisia

Keywords:

(1) measure of
noncompactness

(2) Proinov type contraction

(3) Nonlinear integral equations

Abstract

Integral and differential equations in engineering models are studied using fixed-point methods to analyze the existence of solutions. Darbo [3] presented a generalization of the Schauder fixed point principle by using measures of noncompactness. Later, Sadovskii investigated a new result for condensing mappings. In recent times, there has been a significant increase in research on generalizations of Darbo's theorem and its applications [1, 2, 4]. In [5], Ur Rehman et al. established new results for $\alpha\beta\gamma$ and $\alpha\beta\gamma$ condensing mappings on bounded subsets of Banach spaces. In this paper, we introduce a novel type of contraction mapping in Banach spaces and establish some fixed-point theorems for the sum of two mappings. As an application, we study the existence of fractional integral equations of a given order and provide examples to illustrate our results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] A. Aghajani and R. Allahyari and M. Mursaleen, A generalization of Darbo's theorem with application to the solvability of system of integral equation, J. Comput. App. Math, 260 (2014), 68-77.

[2] H.K. Nashine and R. Ibrahim and R. Arab and M. Rabbani, Generalization of Darbo-Type fixed point theorem and applications to integral equations. In : *Advances in Metric Fixed Point Theory and Applications*. Singapore: Springer Singapore, (2021) 333-364.

[3] G. Darbo, Punti uniti trasformazioni a codeminio non campatto, Rend. Sem. Mat. Padova, 24 (1955) 84-92.

[4] P. D. Proinov, Fixed point theorems for generalized contractive mappings in metric spaces, J. Fixed Point Theory App, 22 (2020) 1-27.

[5] H. ur Rehman and D. Gopal and P. Kumam, Generalizations of Darbo's fixed point theorem for new condensing operators with applications to a functional integral equation, J Demonstr. Math, 52 (2019) 166-182.
Continuous propagation of panic in flight:
Modelling, analysis and optimal time control

**Communication Info**

**Authors:**

Yassine KHOULDI¹
Nadia IDRISSI FATMI¹
Ayoub ABDELALIM¹

¹ LIPIM Laboratory ENSA
Khouribga, Sultan Moulay
Slimane University, Beni Mellal,
Morocco

**Keywords:**

(1) Safety

(2) Propagation

(3) Optimal control

**Abstract**

This work examines the propagation of panic among airline passengers using a continuous SIR model [1]. We apply Pontryagin's maximum principle to design and implement effective control strategies with the main aim of minimizing the number of panicked passengers during the flight. The SIR model, divided into three categories-susceptible, panicked and recovered passengers - was simulated using MATLAB. The results demonstrate the significant effectiveness of the controls implemented, underlining their vital role in maintaining flight safety. Without these measures, the number of panicked passengers could reach critical levels, posing a considerable risk to flight safety. In addition, our simulations have identified the optimal timing for the application of these control measures, a factor that considerably enhances their effectiveness [2,3].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Ayoub Abdelalim, Nadia Idrissi Fatmi, Yassine Khouldi, Analysis and optimal control time for a continuous panic propagation in in-flight scenarios, Commun. Math. Biol. Neurosci., 2024(53), 2024, 1--15.

[2] M. Lafif, A. Ghazaoui, M. Rachik, et al., Study of an optimal control model for the panic propagation in a flying aircraft, Commun. Math. Biol. Neurosci., 2022, 2022, 91.

[3] F.H. Wilhelm, W.T. Roth, Clinical characteristics of flight phobia, J. Anxiety Disord., 11, 1997, 241-261.
<figure><img src="image_25.png" /></figure>

# The generalized of 2-frame in 2-Hilbert space

**Communication Info**

**Authors:**

Samira TATOUTI¹

Nordine Bounader²

¹ Ibn Tofail University,
Kenitra, Morocco.

² Ibn Tofail University,
Kenitra, Morocco.

**Keywords:**

(1) 2-inner Product;

(2) g-2-frames;

(3) g-2-frames operators.

**Abstract**

In the paper, we investigate 2-g-frames a generalization of 2-frames in 2-Hilbert spaces that is compatible with g-frames already known in Hilbert spaces, we will prove a version of the Riesz Representation Theorem in 2-Hilbert space to introduce a definition of g-2-frames, and provide some results concerning this notion. Finally, we will define g-2-frame operators and establish some of their characterizations in 2-Hilbert spaces.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Khosravi, Mathematics and computational sciences, 3, 2022, 10--16.

[2] Harikrishnan, PK and Riyas, P and Ravindran, KT, Novi Sad Journal of Mathematics, 41, 2011, 57--61.

[3] Sun, Wenchang, Journal of Mathematical Analysis and Applications, 322, 2006, 437--452.

[4] Daubechies, Ingrid and Grossmann, Alex and Meyer, Yves, Journal of Mathematical Physics, 27, 1986, 1271--1283.

[5] Duffin, Richard J and Schaeffer, Albert C, Transactions of the American Mathematical Society, 72, 1952, 341--366.
On quantitative stability for parametric equilibria with tri-functions

**Communication Info**

**Authors:**

Asma SAIDI¹

Zakarya MAZGOURI 2

¹Ibn Zohr university, Agadir,
Morocco

²Sidi Mohamed Ben Abdellah
university, Fez, Morocco

**Keywords:**

(1) Equilibrium problems

(2) Holder continuity

(3) Variational inequalities

**Abstract**

Holder continuity is one of the most important concepts of quantitative stability; it serves as a generalization of Lipschitz continuity and has several uses in different mathematical fields [1]. It has been widely studied for parametric equilibrium problems with bifunctions [2]. Unfortunately, equilibrium theory formulated with bi-functions cannot be applied for interesting problems that are not monotone [3]. To overcome this issue, we consider equilibria formulated with trifunctions. More precisely, we suggest an extension of the results in [4], to parametric equilibria with trifunctions.

As applications, we consider Holder continuity for parametric variational inequalities and time-dependent variational inequalities where the constraints set depends on time which also enters as a parameter in the variational formulation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Moudafi. A., Noor. M.A, Sensitivity analysis for variational inclusions by Wiener-Hopf equations technique. J.Appl.Math. Stochastic Anal., 12, 1999, 223-232.

[2] Anh. L.Q., Khanh. P.Q, On the Holder continuity of solutions to parametric multivalued vector equilibrium problems.J. Math. Anal.Appl, 321, 2006, 308-315.

[3] Showalter. R.E, Monotone operators in Banach space and nonlinear partial differential equations. Vol.Mathematical surveys and monographs, Am.Math.Soc, 1997.

[4] Ait Mansour. M., Riahi.H., Sensitivity analysis for abstract equilibrium problems.J. Math. Anal.Appl, 306, 2005, 684-691.

[5] Ait Mansour. M., Mazgouri. Z.,Riahi.H., A dynamical approach for the quantitative stability of parametric bilevel equilibrium problems and applications, Optimization, 71, 2022, 1389-1408.
# Identifying Major Influences on Photovoltaic Panel Efficiency via PCA

## Communication Info

**Authors:**

Abbes KADYRI<fnref n="1" />

Mehdi FARHANE<fnref n="1" />

Khalid KANDOUSSI<fnref n="2" />

Otmane SOUHAR<fnref n="1" />

**Keywords:**

(1) Principal Component Analysis

(2) Photovoltaic Solar Panels

(3) Dimensionality Reduction

## Abstract

The efficiency of photovoltaic solar panels is influenced by numerous factors, including environmental conditions and industrial properties. Identifying the key factors that significantly impact panel efficiency can help manufacturers and installers enhance solar power output. This study employs Principal Component Analysis (PCA) to analyze a comprehensive dataset on solar panel performance, aiming to isolate significant influences. By analyzing a range of climatic and industrial variables, we reduce dimensionality and decipher the predominant factors affecting efficiency. The PCA results reveal that certain environmental factors and design characteristics are the most critical, explaining a substantial portion of the variance in panel performance. These findings corroborate the established understanding of the drivers of solar panel efficiency and highlight the robustness of PCA in processing complex multivariate datasets, thus aiding in the optimization of panel configurations for varying climatic conditions. This approach offers a novel perspective in improving the design and deployment strategies for more efficient solar energy systems globally.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Farhane, Mehdi, Omar Alehyane, and Otmane Souhar. "Three-dimensional analytical solution of the advection-diffusion equation for air pollution dispersion." The ANZIAM Journal 64.1 (2022): 40-53.

[2] Kadyri A., Kandoussi K., Souhar O., An approach on mathematical modeling of PV module with sensitivity analysis: a case study. Journal of Computational Electronics, (2022), 1365-1372.

[3] Kumar, A., Goyal, P.: "Statistical Downscaling of Air Dispersion Model Using Neural Network for Delhi," Centre for Atmospheric Sciences, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India, vol. 16, (2016), pp. 1879-1892.

[4] Souhar, O. and Prud'homme, C.: "Numerical analysis method of heat transfer in an electronic component using sensitivity analysis," Journal of Computational Electronics, vol. 13, (2014), pp.1042-1053.

<footnote n="1">¹ UCD, El Jadida, Morocco</footnote>

<footnote n="2">² ENSA, El Jadida, Morocco</footnote>
# An Enhanced Cuckoo Search Algorithm with Lévy Flight for Efficient High-Order System Reduction

## Communication Info

**Authors:**

Kamel BEN SLIMANE¹

Zied TMAR¹,²

Mongi BESBES ¹,²

¹ University of Tunis El Manar, Tunis, Tunisia

² University of Carthage, Tunis, Tunisia

**Keywords:**

(1) Model Reduction

(2) Cuckoo Search Algorithm

(3) Lévy Flight

(4) Metaheuristic Optimization

(5) Computational Efficiency

(6) System Approximation

## Abstract

This paper presents an enhanced version of the Cuckoo Search Algorithm (CSA) based on Lévy Flight, aimed at reducing the order of high-order systems [1].

The proposed algorithm improves upon the traditional CSA by significantly reducing computational complexity and resource consumption while maintaining high accuracy in the model reduction process [2][3].

By leveraging the Lévy Flight mechanism, the algorithm exhibits better exploration and exploitation capabilities, ensuring faster convergence and superior performance compared to existing methods [4,5,6].

A series of numerical experiments demonstrate the efficiency and effectiveness of the proposed approach in reducing system order while preserving key system dynamics.

The results suggest that this novel version of the CSA provides a promising solution for model reduction in complex systems with large order, making it a valuable tool for both academic research and practical applications.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] B. Ingalls, "Mathematical systems theory i: Modelling, state space analysis, stability and robustness [book review]," Control Systems Magazine, IEEE, vol. 26, pp. 95-97, 2006.

[2] C. Yang, Z. Fan, and Y. Xia, "Convex model-based reduced-order model, for uncertain control systems," IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 705, 2021.

[3] A. K. Prajapati and R. Prasad, "A novel order reduction method for linear dynamic systems and its application for designing of pid and lead/lag compensators," Transactions of the Institute of Measurement and Control, vol. 43, no. 5, pp. 1226-1238, 2021.

[4] A. Joshi, O. Kulkarni, G. Kakandikar, and V. Nandedkar, "Cuckoo search optimization- a review," Materials Today: Proceedings, vol. 4, no. 8, pp.7262-7269, 2017.

[5] K. Sharma, S. Singh, and R. Doriya, "Optimized cuckoo search algorithm using tournament selection function for robot path planning," International Journal of Advanced Robotic Systems, vol. 18, no. 3, 2021.

[6] A. A. Sikander and B. R. Prasad, "A novel order reduction method using cuckoo search algorithm," IETE Journal of Research, vol. 61, no. 2, pp.83-90, 2015.
<figure><img src="image_26.png" /></figure>

Physics-Informed Neural Networks (PINNs): Progress, Challenges
and Future Directions

**Communication Info**

**Authors:**

Mahjoub AAIBID¹ & Jaafar EL KARKRI²

¹,² Mohammed V University in Rabat

*Laboratory LERMA*

*Mohammadia School of Engineers, Rabat, Morocco*

**Keywords** : Physics-informed neural networks (PINNs), Partial differential equations (PDE), Direct and inverse problems, conventional numerical methods, Neural network architectures, Optimization algorithms and techniques, and Loss function composition.

**Abstract**

The main goal of the present work is to provide an in-depth overview framework of the PINNs and their applications in solving direct and inverse problems related to partial differential equations (PDEs).

Although conventional numerical methods have proven effective over time, in many contexts, they can be constrained by various limitations. For high dimensional problems, large-scale computations can be prohibitively expensive due to the dramatic increase in the number of grids. In addition, the implementation of many conventional numerical methods requires full knowledge of the boundaries, initial conditions, and parameters.

Thus, PINNs leverage the flexibility of neural networks to encode physical laws directly into their structure, enabling them to provide solutions without the need for a pre-defined grid. This not only enhances computational efficiency, but also allows greater adaptability to complex boundary conditions and data assimilation tasks. To illustrate these advantages, we use the PINNs to solve a compartmental epidemiological model.

The presentation is organized as follows. The first section covers direct and inverse problems, focusing on conventional numerical methods to solve partial differential equations. The second section presents the PINNs framework and illustrates its application in solving compartmental epidemiological models. Finally, the third section discusses recent advancements in PINNs as well as their main challenges, with a focus on neural network architecture construction, optimization algorithm techniques, loss function composition and the training process.
**Communication Info**

**Authors:**

El Mehdi HASSOUNE ¹
Ahmed JAMEA ¹,²
Abdelghali AMMAR
Adnane KADDIRI¹

¹Equipe des Sciences et
Technologies (ESTE), ENSA,
Université Chouaib Doukkali El
Jadida, Morocco

² CRMEF Casablanca-Settat, S.P. El
Jadida El Jadida, Morocco

**Keywords:**

(1) Degenerate parabolic
problem

(2) Entropy solution

(3) Weighted Sobolev space.

**Abstract**

In this paper, we demonstrate the existence of entropy
solution for some nonlinear degenerate elliptic p(.)-
Laplacian problems associated with Dirichlet-type
boundary condition and right-hand side measure data.
Our primary approach involves leveraging the
variational method in conjunction with the theory of
weighted Sobolev spaces.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Sabri, A. Jamea, H. A. Talibi, Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundar condition in weighted Sobolev spaces, Mathematica Bohemica, Vol. 147, No. 1, pp. 113-129, 202 [2] Authors, Title Journal, Volume, Year, Pages.

[2] M. Sanch\'{o}n, J.M. Urbano: Entropy solutions for the p(x)-Laplace equation. Transactions of the American Mathematical Society 361 (12) (2009) 6387-6405.

[3] V. Mustonen P. Drabek, A. Kufner. Pseudo-monotonicity and degenerated or singular elliptic operators,bull. austral. Math. Soc, (58):213-221, 1998
Statistical inference for a powers stochastic
Rayleigh diffusion process, simulation and
prediction

**Communication Info**

**Authors:**

Abdenbi EL AZRI¹,²

Ahmed NAFIDI²

Abdelkrim MERBOUHA³

¹Higher Institute of Nursing
Professions and Health
Techniques of Casablanca,
Casablanca, Morocco

²Hassan First University of
Settat, National School of
Applied Sciences, Laboratory of
Systems Modelization and
Analysis for Decision Support,
Berrechid, Morocco

³Sultan Moulay Slimane
University, Faculty of sciences
and techniques, Department of
mathematics and Informatics,
LMACS, Beni-Mellal, Morocco

**Keywords:**

(1) Stochastic Rayleigh
diffusion process

(2) Simulation

(3) Fitting and prediction

**Abstract**

In this work, we study a new family of stochastic
diffusion processes, defined by the power of the
inhomogeneous Rayleigh process (see, [1]), which we
term the powers of the stochastic Rayleigh diffusion
process. We first define the new processes, then, the
probabilistic characteristics of the process are
examined, with particular attention to its analytic
expression (see, [2]), transition probability density
function and mean functions. Otherwise, the parameters
that appear in the present process are estimated by
maximum likelihood with discrete sampling (see, [3,5]).
Finally, we will apply this family of processes to
simulated examples, highlighting opportunities for
fitting and prediction (see, [4]).

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Nafidi, Y. Chakroune, R. Gutiérrez-Sánchez, A. Tridane, Forecasting the active cases of covid-19 via a new stochastic Rayleigh diffusion process, Fractal and Fractional, 7 (9), 2023, 660.

[2] L. Arnold, Stochastic Differential Equations, John Wiley and Sons, New York, 1973.

[3] P. W. Zehna, Invariance of maximum likelihood estimators, The Annals of Mathematical Statistics, 37(3), 1966, 744.

[4] C. D. Lewis, Industrial and Business Forecasting Methods: A Practical Guide to Exponential Smoothing and Curve Fitting, Butterworth Scientific, London, 1999.

[5] A. Nafidi, A. El Azri, R. Gutiérrez-Sánchez, A Stochastic Schumacher Diffusion Process: Probability Characteristics Computation and Statistical Analysis, Methodology and Computing in Applied Probability, 25, 2023, 66.
<figure><img src="image_27.png" /></figure>

Existence Results for Nonlinear Parabolic Problems
with Lower Order Terms in Musielak-Orlicz Spaces

**Communication Info**

**Authors:**
Abdeslam TALHA

Hassan First University of
Settat, Faculty of sciences and
Techniques, Laboratory MISI, 26000,
Settat, Morocco.

**Keywords:**

(1) Musielak-Orlicz-Sobolev Spaces

(2) Nonlinear parabolic equations

(3) Poincaré inequality

**Abstract**

In this work, we prove an existence result of renormalized solutions in Musielak-Orlicz -Sobolev spaces for a class of nonlinear parabolic equations with two lower order terms and L1-data. Precisely we consider the following problem:

$$ \frac{\partial u}{\partial t} + A(u) - \operatorname{div}(\Phi(u)) + g(u)\varphi(x, |\nabla u|) = f $$

where $\Omega$ is a bounded Lipchitz open subset of $\mathbb{R}^N$ ($N \ge 2$) which satisfies the segment propriety, $Q = \Omega \times (0, T)$ and $A(u) = -\operatorname{div}(x, t u, \nabla u)$ is a Leray-Lions operator defined on $A: D(A) \subset W_0^1 L_\varphi(Q) \to W^{-1,x} L_\psi(\Omega)$ where $\varphi$ and $\psi$ are two complementary Musielak-Orlicz functions, the right-hand side $f \in L^1(Q)$, we assume that $g$ is an integrable function in $\mathbb{R}$ and satisfying the sign condition, while the function $\Phi$ is a continuous function on $\mathbb{R}$.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Ait Khellou and A. Benkirane, Elliptic inequalities with L1 data in Musielak-Orlicz spaces, Monatsh Math 183 (2017), 1-33.

[2] Blanchard, D. and Murat, F., Renormalized solutions of nonlinear parabolic with L1 data: existence and uniqueness.s Proc. Roy. Soc. Edinburgh Sect, A 127, , (1997), 1137-1152.

[3] A. Benkirane and M. Sidi El Vally, Variational inequalities in Musielak-Orlicz-Sobolev spaces, Bull. Belg. Math. Soc. Simon Stevin 21 (2014), 787-811.

[4] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer, Berlin, 1983.

[5] Talha, A. and Benkirane, A. and Elemine Vall, M.S.B., Entropy solutions for nonlinear parabolic inequalities involving measure data in Musielak-Orlicz-Sobolev spaces, Bol. Soc. Paran. Mat. v.36 2 (2018), 199-230

[6] Talha, A., Benkirane, A., Strongly nonlinear elliptic boundary value problems in Musielak-Orlicz spaces. Monatsh Math 184, 1-32 (2017)
# Stochastic Processes as Classification Algorithms in Stock Market Prediction

## Communication Info

**Authors:**

Mohammed Bouasabah

Ibn Tofail University

**Keywords:**

(1) Stochastic processes

(2) Market prediction

(3) Classification algorithms

## Abstract

Stock market prediction remains a challenging task due to the inherent randomness and complexity of financial data. In this study, we explore the use of stochastic processes as classification algorithms to predict the next-day market trend (up or down) [1]. Specifically, we evaluate the performance of three well-known stochastic models: Geometric Brownian Motion (GBM), the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model [2]. These models are applied to a dataset consisting of three sectoral exchange-traded funds (ETFs): XLF, XLK, and XLV [3]. To assess the effectiveness of each stochastic process in trend classification, we employ common performance metrics, including Precision, Recall, and F1-score [4]. The results provide insights into the suitability of stochastic processes for financial market classification tasks and highlight the comparative strengths and weaknesses of each approach.[5]

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Bouasabah, Mohammed. 2024. A Performance Analysis of Stochastic Processes and Machine Learning Algorithms in Stock Market Prediction. Economies 12: 194. https://doi.org/10.3390/economies12080194

[2] Chandrika, G. Naga, Sai Venkata Rohit Gumudavelli, Ashish Kalleru, Vijitha Kambhampati, and Pragnika Kandaggatlta. 2023. Comparative analysis of machine learning algorithms to forecast indian stock market.

[3] Bouasabah, Mohammed. 2024. Analysis of machine learning's performance in stock market prediction, compared to traditional technical analysis indicators. International Journal of Data Analysis Techniques and Strategies 16: 32-46.

[4] Carvalho, Diogo V., Eduardo M. Pereira, and Jaime S. Cardoso. 2019. Machine learning interpretability: A survey on methods and metrics. Electronics 8: 832

[5] Bonaccorso, Giuseppe. 2017. Machine Learning Algorithms: A Reference Guide to Popular Algorithms for Data Science and Machine Learning. Birmingham and Mumbai: Packt.
Reinforcement Learning-Based Pole Placement for Complex Dynamic
Systems: A Feasibility-Oriented Approach Reduction

**Communication Info**

**Authors:**

Kamel BEN SLIMANE¹

Zied TMAR¹,²

Mongi BESBES 1,2

¹ University of Tunis El Manar,
Tunis, Tunisia

² University of Carthage, Tunis,
Tunisia

**Keywords:**

(1) Reinforcement Learning

(2) Pole Placement

(3) Complex Dynamic Systems

(4) Control Theory

(5) Feasibility-Oriented Design

**Abstract**

Traditional pole placement techniques in control theory primarily focus on the mathematical computation of pole locations without considering their physical feasibility in real-world systems [1].

This limitation can lead to control designs that, while theoretically optimal, fail to meet practical constraints such as stability margins, energy efficiency, and implementation feasibility [2].

This paper proposes a novel strategy for adjusting the dynamics of complex systems through reinforcement learning (RL) [3,4]. By leveraging the reward system inherent in RL algorithms, the proposed approach optimizes pole placement not only from a mathematical perspective but also by ensuring that the resulting system dynamics align with practical operational constraints [5].

The effectiveness of this methodology is demonstrated through simulations on benchmark dynamic systems, showcasing improved adaptability and robustness compared to conventional pole placement methods.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] N. S. Nise, Control systems engineering, 8th Edition, John Wiley & Sons, 2020.

[2] S. Dong and Y. C. Chen, "Analysis of Feasible Synchronverter Pole-Placement Region to Facilitate Parameter Tuning," in IEEE Transactions on Energy Conversion, vol. 36, no. 4, pp. 2782-2793, Dec. 2021.

[3] K. Ben Slimane, Z. Tmar, and M. Besbes, "Deep reinforcement learning LQR controller design for MIMO systems applied to gas production facility," International Journal of Automation and Control, vol. 19, no. 1, 2025.

[4] B. B. Elallid, N. Benamar, A. S. Had, T. Rachidi, N. Mrani, A comprehensive survey on the application of deep and reinforcement learning approaches in autonomous driving, Journal of King Saud University- Computer and Information Sciences 34 (9) 7366-7390, 2022.

[5] N. P. Lawrence, P. D. Loewen, S. Wang, M.G. Forbes, R. B. Gopaluni, Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior, Automatica, Vol. 164, 111642, ISSN 0005-1098, 2024.
<figure><img src="image_28.png" /></figure>

Applications of Variational Inequality and
Reaction-diffusion Equations in Epidemiology

**Communication Info**

**Authors:**

Omar Elamraoui¹

EL Hassan Essoufi¹

Abderrahim Zafrar²

¹ Univ. Hassan 1, Laboratory
MISI, 26000 Settat, Morocco

² Sidi Mohamed Ben
Abdellah University, Faculty
of Sciences Dhar el
Mahraz, Department of
Mathematics, Fes, Morocco

**Keywords:**

(1) SIR model,

(2) Variational inequality,

(3) Uzawa algorithm.

**Abstract**

This work studies some nonlinear variational inequalities with typical operators defined on the reflexive and separable Banach spaces and verifies the uniform monotone and pseudomonotone properties. This study yields some new results, such as the existence and strong convergence of solutions, all based on the Galerkin method. An application of this framework has been given in epidemiology problems considering the Spatio-temporal SIR model which is defined as a reaction-diffusion system. In such application Signorini boundary condition is considered for Infected individuals while Neumann boundary condition is considered for Susceptible and Recovered individuals. The work is ended with numerical analysis of the problem by applying splitting method and Uzawa algorithm based on augmented Lagrangian method. Some tests are included to show the solutions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] B. T. Kien, X. Qin, C.-F. Wen, and J.-C. Yao. The galerkin method and regularization for variational inequalities in reflexive banach spaces. Journal of Optimization Theory and Applications, 189(2):578-596, 2021.

[2] D. P. Bertsekas. Constrained optimization and Lagrange multiplier methods. Academic press, 2014.

[3] E. Bertuzzo, R. Casagrandi, M. Gatto, I. Rodriguez-Iturbe, and A. Rinaldo. On spatially explicit models of cholera epidemics. Journal of the Royal Society Interface, 7(43):321-333, 2010.

[4] A. Bnouhachem, M. A. Noor, M. Khalfaoui, and Z. Sheng. On a new numerical method for solving general variational inequalities. International Journal of Modern Physics B, 25(32):4443-4455, 2011.
**Communication Info**

**Authors:**

Mohcine EL BAROUDI¹

Hassan LAARABI¹

Samira ZOUHRI¹

Mostafa RACHIK¹

Abdelhadi ABTA ¹,²

¹ LAMS, Hassan II University of Casablanca, Faculty of Sciences Ben M'sik, Casablanca, Morocco

² Poly-disciplinary Faculty, Cadi Ayyad University, Safi, Morocco

**Keywords:**

(1) Stochastic optimal control

(2) Stochastic differential equation

(3) SEIR model

(4) Stochastic maximum principle

**Abstract**

This study evaluates the effectiveness of mask-wearing and proactive screening in mitigating the transmission of an epidemic after its onset. Unlike previous research that emphasizes costly interventions such as travel restrictions and vaccination programs [1], this analysis focuses on accessible measures like mask-wearing and proactive testing. A stochastic SEIR (Susceptible-Exposed-Infected-Recovered) model is developed, incorporating control variables for mask-wearing and active screening [2]. By applying a stochastic version of Pontryagin's maximum principle [3], the study aims to identify optimal strategies for implementing these controls. The solution methodology combines the Forward-Backward Sweep Method with a customized Runge-Kutta scheme specifically designed for stochastic differential equations. The findings indicate that, even after the initiation of disease transmission, the simultaneous implementation of mask-wearing and active screening can significantly reduce the number of exposed and infected individuals, offering a cost-effective strategy for resource-constrained nations [4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Okuonghae, D., Oname, A., Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria. *Chaos, Solitons and Fractals*, 139, 2020, 110032.

[2] Kermack, W.O., McKendrick, A.G., Contributions to the mathematical theory of epidemics part 1. *Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences*, 115, 1927, 700-721.

[3] Roshanfekr, M., Farahi, M.H., Rahbarian, R.A., Different approach of optimal control on an HIV immunology model. *Ain Shams Engineering Journal*, 5, 2014, 213-219.

[4] Angstmann, C.N., Henry, B.I., McGann, A.V., A Fractional Order Recovery SIR Model from a Stochastic Process. *Bulletin of Mathematical Biology*, 78, 2016, 468-499.
<figure><img src="image_29.png" /></figure>

# Stochastic Modeling of Disease Spread: SIS Model

**Communication Info**

**Authors:**

Mohamed Rafik¹ Faculty of Science, Ibn Zohr University, Agadir, Morocco

Younes El Ansari¹ Faculty of Science, Ibn Zohr University, Agadir, Morocco

**Keywords:**

(1) SIS model

(2) Stochastic differential equation (SDE)

(3) Epidemic model

**Abstract**

We present a stochastic SIS epidemic model formulated as an SDE, incorporating randomness in the transmission rate. We derive conditions for disease extinction and persistence based on a stochastic basic reproduction number. We establish the existence of a unique positive solution.

We find that persistence occurs when the stochastic reproduction number is greater than one, while extinction is possible when it is less than or equal to one.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] X. Mao, Stochastic Differential Equations and Applications, Elsevier Science, (2008).

[2] E. Allen, Modeling with Itô Stochastic Differential Equations, Springer-Verlag, Dordrecht, The Netherlands, 2007.

[3] L.J.S. Allen, An Introduction to Mathematical Biology, Prentice-Hall, Upper Saddle River, NJ, 2007.
<figure><img src="image_30.png" /></figure>

# Comparison of Bayesian and Frequentist Approaches in Nominal Item Response Theory Modelling

## Communication Info

**Author:**
Olayiwola Matthew ADETUTU

Federal University of
Technology, Minna, Nigeria

**Keywords:**

(1) Bayesian

(2) Frequentist

(3) Nominal

## Abstract

The research utilized a non-linear regression model to quantify unobserved characteristics of candidates in examinations and their outcomes [1]. Performances of Bayesian over Frequentist approaches in estimating nominal item response theory model parameters

$$P(y_{ij} = k | a_i, b_i, \theta_j) = \frac{\exp\{a_{ik}(\theta_j - b_{ik})\}}{\sum_{h=1}^{4} \exp\{a_{ih}(\theta_j - b_{ih})\}}, \quad \theta_j \sim N(0,1) \quad [2]. \text{ Priors}$$

$$a_{ik} \sim \text{dnorm}(m.a, pr.a)I(0,0), b_{ik} \sim \text{dnorm}(m.b, pr.b), m.a \sim \text{dnorm}(0,0.1), m.b \sim \text{dnorm}(0,0.1)$$

pr.a ~ digamma(10,1) and pr.b~digamma(10,1) were used to determine the posterior densities and Brooks-Gelman-Rubin Convergence Diagnostic Statistic suggested 10000 updates to have valid estimates of the intended parameters in accordance to [4]. Findings revealed that Bayesian technique gave positives, and interpretable item discriminating parameters with relatively low standard errors, and more confined credible intervals for the parameters' estimates in line with the principle of item response theory modelling [5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Adetutu, O. M. On Unobserved Traits and Its Measurements: A Note on Modern Item Response Modelling Approach, Proceedings of International Conferences on Mathematical Modelling Optimization and Analysis of Diseases Dynamics (ICMMOADD) 1 (1), 2024, 493-500
https://mathmodel.com.ng/ojs-3405/index.php/icmmoadd

[2] Bock, R. D. Estimating Item Parameters and Latent Ability When the Response are scored in Two or More Nominal Categories. Psychometrika, 37(1972), 29-51.

[3] Hassan, M. U., & Miller, F. Discrimination with Unidimensional and Multidimensional Item Response Theory Models for Educational Data. Communications in Statistics - Simulation and Computation 49(12), (2019), 3299-3313, https://doi.org/10.1080/03610918.2019.1705344

[4] Adetutu, O. M., & Lawal, H. B. Applications of Item Response Theory Models to Assess Item Properties and Students' Abilities in Dichotomous Responses Items. Open Journal of Educational Development (ISSN: 2734-2050), 3(1), (2023) 01-19. https://doi.org/10.52417/ojed.v3i/.304

[5] Lim, S. Review: A Course in Item Response Theory and Modeling with Stata, and Using R for Item Response Theory Model Applications. Structural Equation Modeling: A Multidisciplinary Journal. 27(4), (2020) 657-659, https://doi.org/10.1080/10705511.2020.1740886
An Extension of Young's Inequality in the
Framework of s-Convex Functions

**Communication Info**

**Authors:**

Lahcen TARIK¹

¹ Ibn Tofail University, Kenitra,
Morocco

**Keywords:**

(1) Young's inequality

(2) s-convex functions,

(3) Hermite-Hadamard
inequalities.

**Abstract**

Young's inequality[1,2] is a fundamental result in
mathematical analysis, widely used in optimization and
inequality theory [3]. In this talk, we present a
nontrivial version of this inequality, which we refer to as
the *s-Young inequality*, based on the notion of s-
convexity in the second sense [4]. Our approach relies
on the use of Hermite-Hadamard inequalities for s-
convex functions in second sense [5] to establish this
new form of Young's inequality. We will outline the
central ideas of the proofs and highlight the key steps in
their development.

**Keywords:** Young's inequality, s-convex functions, Hermite-Hadamard inequalities.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Young W. H., "On classes of summable functions and their Fourier series", Proceeding of the Royal Society A, **87**, 1912, pp.225-229.

[2] Moharana, R, "Review on young's inequality", MSc thesis, Dissertation for Ph.D. Degree. Rourkela: National Institute Of Technology, 2014.

[3] T. Valkonen, "Regularisation, optimisation, subregularity." Inverse Problems, **37**(4), 2021, 045010.

[4] H. Hudzik and L. Maligranda, "Some remarks on s-convex functions", Aequationes Math., **48**, 1994, pp.100-111.

[5] S. S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstratio Math., **32**(4), 1999, pp.687-696.
<figure><img src="image_31.png" /></figure>

# Gaussian and Rank-based Optimal Tests for Non-Linear Regression Model

**Communication Info**

**Authors:**

Dounia BOURZIK¹
Abdelhadi AKHARIF¹
Aziz LMAKRI²
Amal MELLOUK³

¹ LMA, FSTT, Abdelmalek Essaadi University, Tetouan, Morocco.

² AICSE laboratory, ENSAM, Hassan II University, Casablanca, Morocco.

³ Regional Center for Education and Training Trades, Tangier, Morocco.

**Keywords:**

(1) Local asymptotic normality

(2) Gaussian tests

(3) Rank tests

**Abstract**

In this paper, we identify a non-linear regression model by proposing both parametric and nonparametric tests that are locally and asymptotically optimal. These tests are specifically designed to evaluate whether the null hypothesis of a traditional linear regression model can be rejected in favor of a non-linear regression model, utilizing the Local Asymptotic Normality (LAN) property. The effectiveness of the proposed tests is validated through numerical simulations, which demonstrate that the Wilcoxon version of rank-based tests consistently outperforms Gaussian parametric tests.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Lmakri, A. Akharif and A. Mellouk, Optimal Detection of Bilinear Dependence in Short Panels of Regression Data, Revista Colombiana de Estadística - Theoretical Statistics, 43(2020): 143-171.

[2] L. M. Le Cam, Asymptotic Methods in Statistical Decision Theory, Springer-Verlag, New York, 1986.

[3] M. Fihri, A. Akharif, A. Mellouk and M. Hallin, Efficient pseudo-Gaussian and rank based detection of random regression coefficients, Journal of Nonparametric Statistics, 32(2020): 367-402.

[4] M. Hallin and B. Werker, Semi-parametric efficiency, distribution-freeness and invariance, Bernoulli, 9(2003): 137-165.
# ANALYSIS OF THE STABILITY OF A MATHEMATICAL MODEL FOR MEASLES

**Communication Info**

**Authors:**

Hicham GOURRAM<fnref n="1" />

Issam SAHIB<fnref n="1" />

Mohamed BAROUDI<fnref n="1" />

Imane SMOUNI<fnref n="1" />

Abderrahim LABZAI<fnref n="2" />

Mohamed BELAM <fnref n="1" />

**Keywords:**

(1) Measles

(2) Control optimal

(3) Pontryagin's maximum principle.

**Abstract**

The worldwide measles crisis has escalated into a significant public health issue due to its lethal nature, generating widespread anxiety. Our study presents a dynamic mathematical model constructed using comprehensive mortality data from the World Health Organization and actual data on measles outbreak propagation. By utilizing the Routh-Hurwitz criteria and formulating Lyapunov functions, we demonstrated both local and global stability for scenarios with and without the presence of the disease. Furthermore, we conducted a sensitivity analysis on the model's parameters to assess their impact on the basic reproduction number, ${R_0}$$. Our theoretical results were substantiated through numerical simulations performed with MATLAB.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Abderrahim Labzai, Bouchaib Khajji, Omar Balatif, Mostafa Rachik. Discrete mathematical modeling of the propagation of religious ideas: Optimal control approach.

[2] Abderrahim Labzai, Omar Balatif, Mostafa Rachik. Optimal Control Strategy for a Discrete Time Smoking Model with Specific Saturated Incidence Rate.

[3] Omar Balatif, Abderrahim Labzai, Mostafa Rachik. A Discrete Mathematical Modeling and Optimal Control of the Electoral Behavior with regard to a Political Party.

[4] Labzai, A., Kouidere, A., Khajji, B., Balatif, O., Rachik, M. Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model. Discrete Dynamics in Nature and Society this link is disabled, 2020, 2020, 5671493.

[5] El Mansouri, A., Labzai, A., Belam, M., Rachik, M. MATHEMATICAL MODELING AND OPTIMAL CONTROL STRATEGY FOR THE OBESITY EPIDEMIC. Communications in Mathematical Biology and Neuroscience, 2022, 2022, 20.

<footnote n="1">¹ Laboratory LMACS, Sultan Moulay Slimane University, MATIC Research Team: Applied Mathematics and Information and Communication Technologie, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco.</footnote>

<footnote n="2">² Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University of Casablanca, Morocco.</footnote>
# Moments Method of Estimation for Diffusion Processes with Random effects driven by Fractional Brownian Motion with Real Application

## Communication Info

**Authors:**

Mohammed ER-RACHIDI¹
Hamid EL MAROUFY¹
Mohamed El OMARI²

¹ Faculty of Science and Technology,
Sultan Moulay Slimane University,
Béni-Mellal, Morocco

² Polydisciplinary Faculty of Sidi
Bennour, Chouaib Doukkali
University, El Jadida, Morocco

**Keywords:**

(1) Random effects

(2) Method of moments

(3) Geometric Fractional Model

## Abstract

The method of moments is a very popular estimation procedure to be applied when likelihood-based methods are difficult to implement, which is the case of the present work. We are concerned with the estimation of the unknown population parameters of the common distribution of random effects from stochastic differential equations driven by a fractional Brownian motion. Based on method of moments we formulate consistent estimators of these parameters and examine their asymptotic normality. We demonstrate their performance by numerical simulations. As an illustration, we apply the method to real Asian financial data. Supplemental material for the article is available online.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Xiao, Weilin and Zhang, Weiguo and Zhang, Xili, Journal of Statistical Computation and Simulation, 85, 2015, 269–283.

[2] Delattre, Maud and GENON-CATALOT, VALENTINE, Scandinavian Journal of Statistics, 40, 2013.

[3] El Omari, Mohamed and El Maroufy, Hamid and Fuchs, Christiane, Statistics, 53, 2019.

[4] Mandelbrot, Benoit B and Van Ness, John W, SIAM review, 10, 1968.

[5] Dufitinema, Josephine and Pynnonen, Seppo and Sottinen, Tommi, Communications in Statistics-Simulation and Computation, 9, 2022.
<figure><img src="image_32.png" /></figure>

Optimal control problem for a bilinear vibrating plate equation
with bounded distributed controls

**Communication Info**

**Authors:**

Tawfik JABER¹

Omar BALATIF 2

¹ Faculty of sciences, Chouaib doukkali University, El Jadida, Morocco.

² Faculty of sciences, Chouaib doukkali University, El Jadida, Morocco.

**Keywords:**

(1) Bilinear systems.

(2) Plate equation.

(3) Gradient problem.

**Abstract**

Our aim is to investigate the gradient tracking problem of a bilinear vibrating plate equation evolving in a spatial domain excited by bounded distributed control acts on the velocity term. We minimize a specified functional cost constituted of the deviation between a target gradient state and the reached one and the energy term. Hence, we prove that an optimal control exists, and we give a characterization of it using an optimality system argument. Moreover, we discuss two additional cases of control sets, space and time one. The given simulation illustrates the theoretical approach by minimizing the gradient plate state using an optimal control in different spaces.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Bradley and S. Lenhart, Bilinear optimal control of a Kirchhoff plate, Systems and Control Letters,1994, 27—38.

[2] M. Bradley and S. Lenhart, Bilinear spatial control of the velocity term in a Kirchhoff plate equation, Electronic Journal of Differential Equations, 2001.

[3] E. Zerrik, A. Ait Aadi, and M. Ouhafsa, On the gradient tracking problem for a bilinear reaction-diffusion equation excited by distributed bounded controls, Journal of Control and Decision, 2022, 1--9.
Exponential decay for mild solutions of second order integro-differential equations with delay

**Communication Info**

**Authors:**

Nebghouha Mohamed
Abdoulay Sene
Moustapha Dieye

¹ Université Cheikh Anta Diop,
Dakar, Senegal

² Université Cheikh Anta Diop,
Dakar, Senegal

³ Ecole polytechnique de Thies,
Thies, Senegal,

**Abstract**

This work led to the development of a special type of second-order evolution equation, specifically integro-differential equations with delay in a Hilbert space $H$. Certain conditions are provided that guarantee the existence of a resolvent operator, which is a key mathematical tool in solving such equations. As a result, the asymptotic behavior of solutions can be analyzed and understood. An example of our method's effectiveness is provided.

**Keywords:**

(1) Integro-differential equations with delay

(2) Hilbert spaces

(3) Exponential stability

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Grimmer R. C., Resolvent operators for integral equations in a Banach space, Transactions of the American Mathematical Society, vol 273, (1982) pp. 333-349.

[2] Ait Ben Hassi E. M, Ammari K., Boulite S. and Maniar L., Feedback stabilization of a class of evolution equations with delay. J. Evol. Equ. vol 9, (2009) pp. 103-121.

[3] Ammari K. and Tucsnak M., Stabilization of second order evolution equations by a class of unbounded feedbacks, ESAIM COCV. vol 6, (2001), pp. 361-386.

[4] H. Brézis, Analyse Fonctionelle : Theorie et Applications, Massons, Paris, (1987), 2ième Edition.

[5] Alabau-Boussouira and P. Cannarsa, "A general method for proving sharp energy decay rates for memory-dissipative evolution equations," Comptes Rendus de l'Académie des Sciences-Series I. Paris, vol. 347, no. 15-16, (2009) pp. 867-872.
Analysis of the Dynamical Behavior of a
Stochastic SEIS Epidemic Model with Nonlinear

**Communication Info**

**Authors:**

Abdelatif KARIMINE¹
Zuhair BEHRAOUI ²
Regragui TAKI ³,

¹ FSJ, El Jadida, UCD, Morocco

² EST, Sidi Bennour, UCD,
Morroco

³ FSJES, Salé, UM5, Morocco

**Keywords:**

(1) Stochastic epidemic model

(2) Extinction

(3) Persistence

(4) Stationary distribution

**Abstract**

In this study, we analyze a stochastic SEIS epidemic model with nonlinear innate immunity under the influence of white noise. We first prove the existence and uniqueness of a global positive solution for the proposed system, ensuring the well-defined behavior of the model over time. Then, we established sufficient conditions for the extinction and persistence in mean of the infectious disease. Moreover, by formulating a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the model's solution. Finally, the theoretical results are verified by some numerical simulations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Jain, S. Kumar. Dynamic analysis of the role of innate immunity in SEIS epidemic model. Eur. Phys J. Plus 136, 439 (2021).

[2] J. M. Liu and F. Y. Wei, "Dynamics of stochastic SEIS epidemic model with varying population size," Physica A: Statistical Mechanics and Its Applications, vol. 464, pp. 241-250, 2016.

[3] M. Naim, F. Lahmidi, and A. Namir, "Treshold dynamics of an SEIS epidemic model with nonlinear incidence rates," Differential Equations and Dynamical Systems, pp. 1-14, 2021.

[4] M. Y. Song, W. J. Zuo, D. Q. Jiang, and T. Hayat, "Stationary distribution and ergodicity of a stochastic cholera model with multiple pathways of transmission," Journal of the Franklin Institute, vol. 357, no. 15, pp. 10773-10798, 2020.

[5] R. Khasminskii, Stochastic Stability of DiFerential Equations, Springer-Verlag, Berlin Heidelberg, Germany, 2nd edition, 2012.
Generalized Common fixed point in fuzzy-metric
spaces and application to an integral equation.

**Communication Info**

**Authors:**

Hamid BEN.HSSAIN<fnref n="1" />

Aziz ELBOUR <fnref n="1" />

Abdelhak EL HADDOUCHI <fnref n="1" />

**Keywords:**

(1) Fuzzy metric spaces

(2) Common fixed point

(3) Implicit relation

(4) Integral equation

**Abstract**

The purpose of this paper is to present a general
common fixed point theorem, which satisfies a specific
implicit relation in fuzzy metric spaces. The results
extend existing theorems and lead to new specific
conclusions. Finally, we highlight the usefulness of
these results by applying them to integral equation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Grabiec, Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 1988, 385-389.

[2] V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 125, 2002, 245-252.

[3] D. Rakić, T. Došenović, Z.D Mitrović, M. de la Sen, S. Radenović, Some fixed point theorems of Ćirić type in fuzzy metric spaces. Mathematics, 8(2), 2020, 297.

[4] T. Žikić, On fixed point theorems of Gregori and Sapena, Fuzzy Sets and Systems 144, 2004, 421-429.

[5] O. Hadžić, A fixed point theorem in menger spaces. Publ. Inst. Math. (Belgr.), 20, 1979, 107-112.

<footnote n="1">¹ Faculty of Sciences and
Technics, Errachidia, Morocco</footnote>
Existence result for a system of ψ-Caputo-type
hybrid fractional differential inclusions

**Communication Info**

**Authors:**

MOHAMED EL FADOUAKI¹
KHALID HILAL¹
AHMED KAJOUNI¹
HAMID LMOU¹

¹ Laboratory of Applied
Mathematics and Scientific
Computing, Sultan Moulay
Slimane University, Beni Mellal,
Morocco

**Keywords:**

(1) Fractional differential
hybrid inclusions

(2) ψ-Caputo fractional
derivative

(3) Fractional differential
inclusions

(4) ψ-Caputo fractional
differential inclusions

**Abstract**

In this paper, we study the existence of solutions to a class of $\psi$-Caputo-type fractional hybrid differential inclusions with nonlocal boundary conditions. We study a fractional order system of derivatives of order $\alpha$ where $1 < \alpha \leq 2$, subjected to integral and discrete multipoint boundary conditions. The study extends previous research [1,2,3] on fractional hybrid differential equations by introducing the $\psi$-Caputo fractional derivative operator [4], which offers enhanced flexibility in modeling complex phenomena. Our primary theoretical mechanism, based on fixed point theory in Banach algebras (Dhage's fixed point theorem [5]), gives existence results in the presence of mixed Lipschitz and Carathéodory conditions. The theory is developed in the setting of multivalued mappings, thus offering a more general treatment of the question. We provide comprehensive theoretical results, featuring existence theorems, and complement our results with examples to illustrate the use of the theoretical results in practice.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Dhage, B. C., Ntouyas, S. K.: Existence results for boundary value problems for fractional hybrid differential inclusions. Topological Methods in Nonlinear Analysis, 44(1), (2014), 229-238.

[2] Hilal, K., Kajouni, A.: Boundary value problems for hybrid differential equations with fractional order. Advances in Difference Equations, 2015(1), 1-19, (2015).

[3] Hilal, K., Kajouni, A., Lmou, H.: Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative. International Journal of Differential Equations, (2022)

[4] R. Almeida, A caputo fractional derivative of a function with respect to another function, Communications in Nonlinear Science and Numerical Simulation 44 (2017) 460–481.

[5] Dhage, B.C.: Existence results for neutral functional differential inclusions in Banach algebras, Nonlinear Anal. 64, (2006), 1290-1306.
**Communication Info**

**Authors:**

Mohammed EDAROUI<fnref n="1" />

Adil BAIZ<fnref n="2" />

Amine FAIZ<fnref n="3" />

Jamal MOULINE<fnref n="4" />

Khadija BOUZKOURA<fnref n="5" />

**Keywords:**

(1) Fixed point

(2) tricyclic diametrically

(3) tricyclic contraction

(4) pointwise tricyclic

**Abstract**

In this article, we are referring to introducing a new class of mappings called tricyclic diametrically contractive mappings, which are defined as the union of triad nonempty subsets of a metric space. The authors provide necessary and sufficient conditions for the existence of the best proximity point for these mappings.

This new class of mappings extends the theory of traditional diametrically contractive mappings and provides a more general framework for studying fixed points and optimization problems in metric spaces. The best proximity point, which is a particular type of fixed point that is closest to a given point in the metric space, is an important tool for solving optimization problems. The results provided in this article represent a significant contribution to the field of analysis and its applications. They are expected to have far-reaching implications for the study of fixed points and optimization problems in metric spaces. The new class of tricyclic diametrically contractive mappings and the conditions for the existence of the best proximity point are likely to be of great interest to researchers in mathematics and science, as well as practitioners in various fields that make use of optimization algorithms.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] V.I. Istratescu, Some fixed theorems for convex contraction mappings and mappings with convex diminishing diameters. IV nonexpansive diameter mappings in uniformly convex spaces, preliminary report. Abstract of the American Mathematical Society, 82T-46-316, (1982).

[2] W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Mon. 72 (1965), 1004-1006. https://doi.org/10.2307/2313345.

[3] H.K. Xu, Diametrically contractive mappings, Bull. Austral. Math. Soc. 70 (2004), 463-468. https://doi.org/10.1017/s0004972700034705.

[4] T. Sabar, M. Aamri, A. Bassou, Best proximity points for tricyclic contractions, Adv. Fixed Point Theory, 7 (2017), 512-523.

[5] E. Mohamed, E.K. Amine, A. Mohamed, Best proximity point theorems for proximal pointwise tricyclic contraction, Adv. Fixed Point Theory, 13 (2023), 22. https://doi.org/10.28919/afpt/8194.

<footnote n="1">¹ FSBM, Casablanca, Morocco</footnote>

<footnote n="2">² FSBM, Casablanca, Morocco</footnote>

<footnote n="3">³ FSBM, Casablanca, Morocco</footnote>

<footnote n="4">⁴ FSBM, Casablanca, Morocco</footnote>

<footnote n="5">⁵ FSBM, Casablanca, Morocco</footnote>
<figure><img src="image_33.png" /></figure>

An extension of Van Velck's functional equation on semigroups

**Communication Info**

**Authors:**

Youssef ASERRAR¹

Elhoucien ELQORACHI ¹

¹ Ibn Zohr University-Faculty of Sciences, Agadir, Morocco

**Keywords:**

(1) Semigroup.

(2) Automorphism.

(3) Measure.

(4) Van Vleck's functional equation.

**Abstract**

Let $S$ be a semigroup, $Z(S)$ the center of $S$. In this paper, we determine the complex-valued solutions of Van Vleck's functional equation

$$\int_S f(xyt)d\mu(t) - \int_S f(\sigma(y)xt)d\mu(t) = 2f(y)g(x), x, y \in S,$$

where $\mu$ is a measure that is a linear combination of Dirac measures $(\delta z_i)_{i \in I}$, such that $z_i \in Z(S)$ for all $i \in I$, and $\sigma: S \to S$ is an involutive automorphism. We also give some interesting consequences.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Aserrar, Y., Elqorachi, E., Kannappan-Wilson and Van Vleck-Wilson functional equations on semigroups. Acta Math. Hungar. 173, 193-213 (2024).

[2] Bouikhalene, B., Elqorachi, E., An extension of Van Vleck's functional equation for the sine. Acta Math. Hungar., 150, no. 1, 258-267 (2016).

[3] Gajda, Z., A generalization of d'Alembert's functional equation. Funkcial. Ekvac. 33(1), 69-77 (1990)

[4] Nagy, B.S., A sine functional equation in Banach algebras. Publ. Math. Debrecen 24(1-2), 77-90 (1977).

[5] Stetkær, H., Van Vleck's functional equation for the sine. Aequat Math., 90, 25-34 (2016).

[6] Van. Vleck, E.B., A functional equation for the sine. Ann. Math. Second Ser., 11 (4), 161-165 (1910).
<figure><img src="image_34.png" /></figure>

Fuzzy Complex Conformable Differentiation

**Communication Info**

**Authors:**

Atimad HARIR

¹ Laboratory of Applied
Mathematics and Scientific
Computing, Ecole Normale
Superieure
Sultan Moulay Slimane
University,
B.P. 523, Beni Mellal,
Morocco

**Keywords:**

(1) Complex Fuzzy numbers

(2) fuzzy conformable
derivative

(3) complex fuzzy
conformable derivatives

**Abstract**

In this paper, some important fuzzy real fractional calculus results are extended to the context of fuzzy complex-valued functions of a real variable. Two conformable derivatives of such functions are defined, which are expansions of [1] conformable derivatives of real fuzzy mappings[4]. Two examples of complex fuzzy conformable derivatives are shown, as well as their features [2,3].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Harir, S. Melliani, L S. Chadli. Fuzzy generalized conformable fractional derivative. Advances in Fuzzy Systems, 2019, volume 2020, Article ID 1954975, 7 pages, https://doi.org/10.1155/2020/1954975.

[2] Z. Guangquan, Fuzzy limit theory of Fuzzy complex numbers, FSS 46 (1992) 227-235.

[3] J. J. Buckley, and Y. Qu, Fuzzy complex analysis I: Differentiation, FSS 41 (1991) 269-284.

[4] A. Harir, S. Melliani and L.S. Generalization of the Fuzzy Conformable Differentiability with Application to Fuzzy Fractional Differential Equations, In book: Intelligent Systems in Big Data, Semantic Web and Machine Learning Edition: 1, Chapter: 9,Pages 125-139,(2021)
<figure><img src="image_35.png" /></figure>

# Stabilité et contrôlabilité des équations aux dérivées partielles d'ordre quatre

## Communication Info

**Authors:**

Yassine EL ISSAOUY¹
Abdelkarim HAJJAJ ²
Brahim ALLAL ³

¹ Université Hassan 1, Settat,
Maroc

² Université Hassan 1, Settat,
Maroc

³ Université Ibn Zohr, Agadir,
Maroc

**Keywords:**

(1) Équations aux dérivées partielles.

(2) Opérateur d'ordre 4.

(3) Stabilité, contrôlabilité.

(4) Semi-groupes d'opérateurs

(5) Stabilité, contrôlabilité.

(6) méthodes de
multiplicateurs

## Abstract

Les équations aux dérivées partielles d'ordre quatre [2] apparaissent naturellement dans divers modèles physiques et mécaniques, notamment dans la théorie des plaques et des poutres en élasticité. Cette présentation est consacrée à l'étude des propriétés analytiques et asymptotiques de ces équations, avec un accent particulier sur la stabilité [1] et la contrôlabilité des solutions. Nous examinerons les méthodes mathématiques modernes permettant d'analyser ces systèmes, en mettant en avant l'approche des semi-groupes d'opérateurs [3], les méthodes de multiplicateurs et les techniques variationnelles. Des exemples concrets, comme l'équation de Petrovsky [4] fortement amortie et les équations de type Euler-Bernoulli, seront discutés pour illustrer les résultats théoriques et leurs applications potentielles.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Salah Boulaaras- Mohammed Saïd Souid, Afrika Matematika, Volume, January 2025, 21.

[2] Truong Thi Nhan, Electronic Journal of Applied Mathematics, 2023, Vol. 1, No. 2, 30.

[3] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, Berlin (1983)

[4] Truong Thi Nhan, Electronic Journal of Applied Mathematics, 2023, Vol. 1, No. 2, 30.
<figure><img src="image_36.png" /></figure>

Counting primitive kth Roots of Unity Modulo n

**Communication Info**

**Authors:**

Abderrahim MAKKI NACIRI

¹ Faculty Semlalia, Cadi Ayyad
University, Marrakesh,
Morocco.

**Keywords:**

(1) Roots of unity

(2) Primitive root of unity

[3] Möbius-inversion
formula

**Abstract**

Given positive integers *n* and *k*, we provide an explicit formula for the number of kth roots of unity modulo *n*, assuming the prime factorization of *n* is known. Furthermore, when the prime factorization of *k* is also available, we explicitly determine the number of primitive kth roots of unity using the Möbius inversion formula. In the case where *n* is a factorial, we provide a bound on the number of square roots modulo *n* without relying on the prime factorization of *n*.

The concept of primitive kth roots of unity is a fundamental tool with numerous applications. In computer science, kth roots of unity are utilized in the Fast Fourier Transform (FFT) algorithm. They also feature prominently in constructing cyclic codes and are employed in pseudorandom number generators.

In cryptography, primitive roots of unity are essential components of public-key protocols, including the Diffie-Hellman key exchange and RSA algorithm. The concept is also closely tied to the discrete logarithm problem.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Finch, G. Martin, and P. Sebah, Roots of unity and nullity modulo *n*, *Proc Am Math Soc* (138) (8), 2010, 2729-2743.

[2] S. Seraj, Counting general power residues, *Notes Number Theory Discrete Math*, (28)(4), 2022, 730-743.

[3] I. Niven, H. S. Zuckerman and H. L. Montgomery, *An Introduction to the Theory of Numbers* (Fifth edition). John Wiley and Sons Inc, New York (1991).
<figure><img src="image_37.png" /></figure>

Translation surfaces generated by two relatively
normal-slant helices in Euclidean 3-space

Communication Info

Authors:

Salma KHAN¹
Malika IZID¹
Abderrazzak El Haimi¹
Bouchra Aharmim¹
Amina OUAZZANI CHAHDI¹

¹LAMS, Faculty of Sciences Ben M'Sick, University Hassan II of Casablanca, Morocco.

Keywords:

(1) Translation surface

(2) *Line of curvature*.

(3) Normal curvature

(4) *Darboux frame*

(5) Relatively normal-slant helix

Abstract

In differential geometry, a translation surface is a
surface obtained by translating a curve α = α(u) along
another curve β = β(v). Translation surfaces can be
locally parametrized by

$$
\varphi(u, v) = \alpha(u) + \beta(v),
$$

where α : I C R → E³ and β : J C R → E³, with E³ a 3-
dimensional Euclidean space.

In this study, we provide parametric representations
and propose illustrative examples of some translation
surfaces, defined by

$$
M : X(u, v) = \alpha(u) + \beta(v),
$$

in the case where the curves $u \rightarrow \alpha(u)$ and $v \rightarrow \beta(v)$
are relatively normal-slant helices for the initial surface
$\Sigma$, provided with their respective Darboux frames.
($T_\alpha$, $V_\alpha$, $U_\alpha$) and ($T_\beta$, $V_\beta$, $U_\beta$), i.e. each of the two vector
fields $V_\alpha$ and $V_\beta$ makes a constant angle with a fixed
direction. We distinguish two cases:

$\alpha$ and $\beta$ relatively normal-slant helices and lines of
curvature for the initial surface $\Sigma$, and in the second
case $\alpha$ and $\beta$ relatively normal-slant helices with
$\tau_{g\alpha} \neq 0$ and $\tau_{g\beta} \neq 0$.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] A. El Haimi, and A. Ouazzani Chahdi, Position Vectors of a Relatively Normal-slant Helix in Euclidean 3-space, Jordan Journal of Mathematics and Statistics (JJMS) 16.1 139-152 (2023).

[2] P. DO-CARMO (1976), Differential Geometry of Curves and Surfaces; IMPA, 511.

[3] A. El Haimi, and A. Ouazzani Chahdi, Parametric equations of special curves lying on a regular surface in Euclidean 3-space, Nonlinear Functional Analysis and Applications 26.2 225-236 (2021).

[4] S. Khan, M. Izid, S. Ouarab, and A. Ouazzani Chahdi, Translation surfaces generated by the spherical indicatrices of Frenet frame of regular curves of 3-dimensional Euclidean space, Boletim da Sociedade Paranaense de Matematica, Vol 43 (2025).

[5] H. Liu, Translation surfaces with constant mean curvature in 3-dimensional spaces, J. Geom. 64 (1999) 141–149.
Stochastic two-strain epidemic model with saturated incidence
rates driven by Lévy noise

**Communication Info**

**Authors:**

Marya SADKI¹

Karam ALLALI¹

¹Laboratory of Mathematics,
Computer Science and
Applications, Faculty of
Sciences and Technologies,
University of Hassan II of
Casablanca, PO Box
146, Mohammedia, Morocco

**Keywords:**

(1) Two-strain

(2) Epidemic model

(3) Extinction

(4) Persistence in mean

(5) White noise

(6) Lévy noise

**Abstract**

In this work, we introduce a stochastic two-strain epidemic model driven by Lévy noise describing the interaction between four compartments; susceptible, infected individuals by the first strain, infected ones by the second strain and the recovered individuals. The forces of infection, for both strains, are represented by saturated incidence rates. Our study begins with the investigation of unique global solution of the suggested mathematical model. Then, it moves to the determination of sufficient conditions of extinction and persistence in mean of the two-strain disease. In order to illustrate the theoretical findings, we give some numerical simulations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. London Ser. A, Contain. Papers Math. Phys. Character **115**(772), 700–721 (1927)

[2] M. Sadki, K. Allali (2024). Stochastic two-strain epidemic model with saturated incidence rates driven by Lévy noise. *Mathematical Biosciences*, **375**, 109262.

[3] M. Sadki, A. Ez-zetouni, K. Allali, Persistence and extinction for stochastic HBV epidemic model with treatment cure rate, Boletim da Sociedade Paranaense de Matemática.

[4] M. Sadki, K. Allali, Stochastic two-strain epidemic model with bilinear and non-monotonic incidence rates, Eur. Phys. J. Plus **138** (10) (2023) 1–15.

[5] M. Sadki, Z., Yaagoub, & K. Allali, (2024). Stochastic analysis of two-strain epidemic model with non-monotone incidence rates: Application to COVID-19 pandemic. *Mathematical Methods in the Applied Sciences*, **47**(11), 8651-8668.
Improved qualitative results for retarded integro-differential equations

**Communication Info**

**Authors:**

Osman TUNÇ

¹ Department of Computer
Programming, Baskale
Vocational School, Van
Yuzuncu Yil University,
Campus, 65080, Van, Turkey

**Keywords:**

(1) Lyapunov-Krasovskiï
functional

(2) Integro-differential
equations

(3) Stability

(4) Boundedness

**Abstract**

This paper focuses on a class of nonlinear time-varying retarded integro-differential equations. Using the Lyapunov-Krasovskiï functional method, we establish some new results under sufficient conditions ensuring uniform stability, uniform asymptotic stability, integrability, and boundedness of solutions to the retarded integro-differential equations. The main novelty and originality of this article are that the considered integro-differential equations with retarded arguments are new mathematical models and the qualitative results given are also new.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Bohner, Martin; Tunç, Osman. Qualitative analysis of integro-differential equations with variable retardation. Discrete Contin. Dyn. Syst. Ser. B 27 (2022), no. 2, 639–657.

[2] Tunç Osman. Stability, instability, boundedness and integrability of solutions of a class of integro-delay differential equations. J Nonlinear Convex Anal 2022;23(4):801–19.

[3] Tunç, Osman; Tunç, Cemil; Petruşel, Gabriela; Yao, Jen-Chih. On the Ulam stabilities of nonlinear integral equations and integro-differential equations. Math. Methods Appl. Sci. 47 (2024), no. 6, 4014–4028

[4] Tunç, Cemil; Tunç, Osman; Wen, Ching-Feng; Yao, Jen-Chi. On the qualitative analyses solutions of new mathematical models of integro-differential equations with infinite delay. Math. Methods Appl. Sci. 46 (2023), no. 13, 14087–14103.

[5] Tunç, Cemil; Tunç, Osman; Yao, Jen-Chih. On the stability, integrability and boundedness analysis of systems of integro-differential equations with time-delay. Fixed Point Theory 24 (2023), no. 2, 753–774.
<figure><img src="image_38.png" /></figure>

# Dynamic Conduct of a Stochastic Unemployment
Model

**Communication Info**

**Authors:**

Oumaima AARABATE¹

Omar BALATIF ¹

¹ Laboratory of fundamental
mathematics and their
applications, Faculty of
sciences, University of Chouaib
Doukkali, El Jadida, Morocco

**Keywords:**

(1) Unemployment model

(2) Asymptotically stable in
the large

(3) Stochastic Lyapunov
function.

**Abstract**

In this paper, we propose and analyze a mathematical model with stochastic perturbation of the issue of unemployment by considering three main variables. Namely graduates or individuals who have reached the age of employment, salaried individuals and employees, and then individuals who have been made redundant or who have resigned from work. After the description of the proposed model, we study the existence and the uniqueness of the nonnegative solution. Furthermore, we investigate the asymptotic behavior of this solution by analyzing the stability of the system at the equilibrium points. Finally, some numerical simulations are performed to verify the theoretical analysis using Matlab.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] O. Aarabate, O. Balatif, S. M. Lalaoui Ben Cherif, The study of the asymptotic behavior of the global positive solution to an unemployment model with stochastic perturbation, Mathematics in Science, Engineering, and Aerospace (MESA), 15(3), 2024, 945-960.

[2] X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, UK, 1997.

[3] L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York, 1972.

[4] N. Dalal, D. Greenhalgh, X. Mao, A stochastic model of AIDS and condom use, Journal of Mathematics Analysis and Application. 325(1), 2007, 36-53.
BLOCK COORDINATE DESCENT METHODS OF CENTER

**Communication Info**

**Authors:**

Khaoula Kharfati¹

Ahmed Roubi²

¹ FST, Settat, MOROCCO

² FST, Settat, MOROCCO

**Keywords:**

(1) BCD methods

(2) Method of center

(3) Optimality conditions

**Abstract**

A block coordinate descent method, is an iterative procedure that solves block-structured optimization problems, where each block of coordinates is subject to its own constraints. For such problems, we develop a new method that act by solving less constrained and of smaller size subproblems. We propose, the block coordinate descent method of centers (BCDMC), that solves an unconstrained or at least less constrained problems, which are of smaller size than the original problem. Under regularity properties involving the objective function, we establish optimality conditions on the entire decision variable, based on those established for its block coordinates. These methods generate sequences whose every cluster point satisfies these optimality conditions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Auslender, Asymptotic properties of the Fenchel dual functional and applications to decomposition problems, J. Optim. Theory Appl., Vol. 73, 1992, pp. 427-449.

[2] L. Grippo and M. Sciandrone, On the convergence of the block nonlinear Gauss-Seidel method under convex constraints, Oper. Res. Lett., Vol. 26, 2000, pp. 127-136.

[3] P. Richta_rik and M. Taka_c, Parallel coordinate descent methods for big data optimization, Math. Program., Vol. 156, 2016, pp. 433-484.

[4] A. Roubi, Some properties of methods of centers, Comput. Optim. Appl., Vol. 19, 2001, pp. 319-335,

[5] P. Tseng, Convergence of a block coordinate descent method for nondi_erentiable minimization, JOTA, Vol. 109, 2001, pp. 475-494.
# A Mathematical model for the interaction between Covid-19 and Tuberculosis dynamics

## Communication Info

**Authors:**

BENAMARA Ibtissam¹,²

BENAZZA Hafida ²

FAIZ Mariem ²

¹ SMARTiLab Laboratory,
Moroccan School of
Engineering Sciences (EMSI),
Rabat Morocco.

² Mathematics, Computer
Sciences, and Applications
Information Security
Laboratory (LABMIA-SI),
Faculty of Sciences,
Mohammed V University,
Rabat, Morocco.

**Keywords:**

(1) COVID-19

(2) Tuberculosis

(3) Co-infection

(4) Reproduction number.

## Abstract

This study examines a mathematical model that captures the transmission dynamics of COVID-19 and tuberculosis within a population, emphasizing the interplay between the two diseases. The model incorporates key epidemiological factors, such as co-infection and disease progression, to better understand their joint impact. The existence and uniqueness of the endemic equilibrium are rigorously proven, followed by a comprehensive analysis of the equilibrium points and their local stability. To provide deeper insights, a sensitivity analysis is conducted to identify critical parameters influencing disease dynamics. Finally, numerical simulations are carried out to validate the theoretical results and explore potential scenarios, offering valuable perspectives for public health strategies.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] M. Diagne, H. Rwezaura, S. Tchoumi, J. Tchuenche, A mathematical model of COVID-19 with vaccination and treatment, Comput. Math. Methods Med. 2021 (2021).

[2] M. Kumar, D. Surendran, M. Manu, P. Rakesh, S. Balakrishnan, Mortality of TB-COVID-19 coinfection in India, Int J. TB Lung Dis. (2021) 250-251.

[3] P. Van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (1-2) (2002) 29-48.
**Communication Info**

**Authors:**

Abdelhadi ELHARFI¹
Mustapha EL HASSANI²
Samir El MOURCHID²

¹ Department of Mathematics,
Regional Center for Education
and Training Professions, Sous
Massa, Agadir, Morocco.

² Laboratory of Mathematical
Analysis and Applications, Ibn
Zohr University, Agadir,
Morocco.

**Keywords:**

(1) Backstepping
transformation

(2) the Laplace transform

(3) C_0-semigroup

(4) Green's function

(5) trajectory tracking

**Abstract**

The trajectory tracking problem (TTP) refers to the procedure of finding an input control that steers the system output to follow a predefined path. In this paper, we investigate the TTP for controlled systems governed by a 2-D Heat equation in which we target a perfect matching of the system output with a desired trajectory. The controller as well as the corresponding state response are explicitly given by means of the target trajectory and the solutions of appropriate kernels PDEs. The approach is based on backstepping techniques, the Laplace transform, and Green's functions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Elharfi, M. El hassani and S. El Mourchid, motion planning Problem For a class of hyperbolic PDEs.
Journal of Evolution Equation and Control Theory (EECT), Vol. 12, 2023, pp. 1268-1286

[2] A. Elharfi, Exponential stabilization and motion planning of an overhead crane system; IMA Journal of
Mathematical Control and Information, Vol 34, 2017, pp 1299-1321.

[3] K. Engel and R. Nagel, One-parameter Semigroups for Linear Evolution Equations, Ency-clopedia of
Mathematics and its Applications, Springer-Verlag 2000.

[4] P. Grabowski, The motion planning problem and exponential stabilization of a heavy chain. Part I,
International Journal of Control, Vol. 82, 2009, pp. 1539-1563.

[5] B. Laroche, P. Martin, and P. Rouchon, Motion planning for the heat equation, International Journal of
Robust and Nonlinear Control, Vol. 10, 2000, pp. 629-643.
# On the Robustness of Augmented Box-Behnken Designs to Two Missing Observations

**Communication Info**

**Authors:**

Oluchukwu C. ASOGWA¹

Oluwaseun A. OTEKUNRIN ³

Nnaemeka M. EZE ⁴

¹ Alex Ekwueme Federal
University, Ndufu-Alike, Ebonyi
State, Nigeria

³ University of Ibadan, Ibadan,
Nigeria

⁴ University of Nigeria, Nsukka,
Nigeria

**Keywords:**

(1) Robustness of designs

(2) Missing observations

(3) Third-order designs

**Abstract**

Second-order response surface models might sometimes be inadequate and unfeasible in real-life investigations due to the lack of fit caused by the presence of third-order terms [1]. This willingly opens the door for augmentation of a second-order response surface model to a third-order model. The third-order designs that take care of the estimates of the model in this work are augmented Box-Behnken Designs (ABBDs), which have always been confronted with missing observations [2]. This scenario that has affected the design's power of test and desirable properties, often comes up when observations are lost, or ignored [3]. Therefore, this work developed a minimax loss ABDs robust to two missing observations under minimax loss criterion [4]. The developed robust designs have applications in experimental fields [5, 6].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Rashid, F., Akram, M., Akbar, A., and Javed, A., Some New Augmented Fractional Box-Behnken Designs, *Communications in Statistics-Theory and Methods*, 46, 2017, 2007-2012.

[2] Arshad, H. M., Akhtar, M., and Gilmour, S. G., Augmented Box-Behnken designs for fitting third-order response surfaces, *Communications in Statistics-Theory and Methods*, 41, 2012, 4225-4239.

[3] Patchanok, S., Robust response surface designs against missing observations. *A Ph. D dissertation*, Montana State University, Bozeman, Montana, 2015.

[4] Akram, M., Central Composite Designs Robust to three missing observations, *A Ph. D Thesis in Statistics*, Islamia University, Baha-walpur, Pakistan, 2002.

[5] Safari, M., Abdi, R., Adl, M., and Kafashan, J., Optimization of biogas productivity in lab-scale by response surface methodology. Renewable Energy, 118, 2018, 368-375.

[6] Nwabueze, T. U., Basic steps in adapting response surface methodology as mathematical modelling for bioprocess optimization in the food systems. *International Journal of Food Science and Technology*, 45, 2010, 1768-1776.
Pythagorean Fuzzy Sublattices and Ideals

**Communication Info**

**Authors:**

Meryem FAKHRAOUI¹
Idris BAKHADACH ¹
Said MELLIANI ¹

¹ *Sultan Moulay Slimane*
*University, Beni Mellal,*
*Morocco*

**Keywords:**

(1) Fuzzy Lattice

(2) Pythagorean Fuzzy
Sublattice

(3) Pythagorean Fuzzy
Homomorphism

**Abstract**

This research delves into the exploration of Pythagorean fuzzy sublattices and Pythagorean fuzzy ideals within the context of lattice theory. Through a rigorous analysis of structural theorems concerning these concepts derived from Pythagorean fuzzy sets, we uncover significant parallels with classical theory. Additionally, we investigate the behavior of Pythagorean fuzzy ideals under lattice homomorphisms. Our findings shed light on the applicability and utility of Pythagorean fuzzy theory in lattice-based structures, offering insights into their properties and relationships.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] L.A. Zadeh, Fuzzy sets, Information and control, 8(1965), 338-353.

[2] R.R. Yager, Pythagorean fuzzy subsets, in Proc. Joint IFSA World Conger. NAFIPS Annu. Meeting(IFSA/NAFIPS), Jun.2013, pp.57-61, doi:10.1109/IFSA-NAFIPS.2013.6608375.

[3] Bakhadach, I., Melliani, S., Oukessou, M., & Chadli, L. S. (2016). Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring. Notes on Intuitionistic Fuzzy Sets, 22 (2), (pp. 59-63).

[4] Ajmal N, Thomas K V (1994) Fuzzy lattices. Information Sciences Vol.79: 271-291.

[5] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and system, 20(1986), No.1, 87-96
Qualitative results for intuitionistic fuzzy Cauchy
Problem

**Communication Info**

**Authors:**

El Houssine BOUZID¹

Bouchra BEN AMMA²

Said MELLIANI¹

Lalla Saadia CHADLI ¹

¹LMACS, Faculty of Sciences
and Technologies, Sultan
Moulay Slimane University,
Beni Mellal, Morocco.

² LMACS, Higher School of
Education and Training, Sultan
Moulay Slimane University,
Beni Mellal, Morocco.

**Keywords:**

(1) Intuitionistic fuzzy number

(2) Cauchy Problem

(3) Gronwall's Lemma

(4) Metric space

(5) Fixed point Theorem

(6) Integral equations

(7) Hyers-Ulam stability

**Abstract**

In this study, we will investigate, based on Banach fixed-point Theorem, the existence and uniqueness of a solution to The intuitionistic fuzzy Cauchy Problem (IFCP), by introducing a new metric in the space of intuitionistic fuzzy functions. Using Gronwall's Lemma, some qualitative properties of the solution, and its Hyers-Ulam stability, are also discussed. The new metric introduced in this paper makes the contraction condition easy to obtain. The approach used in this study has a larger domain of applicability, and gives an idea about the behavior of the solution to (IFCP), which can help us to develop numerical methods to find an approximate solution.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] K. T. Atanassov, Intuitionistic fuzzy sets. VII ITKR's session, Sofia (deposited in Central Science and Technical Library of the Bulgarian Academy of Sciences 1697/84), 1983.

[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 1986, 87-96.

[3] B. Ben Amma, S. Melliani & L. S. Chadli, The Cauchy problem of intuitionistic fuzzy differential equations, Notes on Intuitionistic Fuzzy Sets, 24, 2018, 37-47.

[4] M. Bohner, P.S. Scindia, & S. Tikare, Qualitative Results for Nonlinear Integro-Dynamic Equations via Integral Inequalities, Qual. Theory Dyn. Syst. 21, 106, 2022.

[5] J. Huang, S.-M. Jung & Y. Li, On Hyers-Ulam Stability Of Nonlinear Differential Equations, Bulletin of the Korean Mathematical Society, 52(2), 2015, 685-697.

[6] S. Melliani, M. Elomari & L. S. Chadli, Intuitionistic fuzzy metric space, Notes on intuitionistic Fuzzy sets, 21, 2015.43-53.
# Stability Analysis of a Mathematical Model for Malaria Transmission

## Communication Info

**Authors:**

FAIZ Mariem¹

BENAZZA Hafida ¹

BENAMARA Ibtissam ¹

TAFTAF Chaimaa ¹

¹ Mathematics, Computer Sciences, and Applications Information Security Laboratory (LABMIA-SI), Faculty of Sciences, Mohammed V University, Rabat, Morocco

**Keywords:**

(1) Malaria

(2) Epidemic model

(3) Disease free-equilibrium

(4) Basic reproduction number

## Abstract

This study analyzes the stability of a mathematical model for malaria transmission, formulated as a system of five differential equations. We examine the local stability of the disease-free equilibrium (DFE) and the endemic equilibrium. Our results establish that the DFE is locally asymptotically stable when the basic reproduction number R0 < 1, implying disease eradication. Conversely, when R0 > 1, the DFE becomes unstable, and the endemic equilibrium is locally asymptotically stable, suggesting disease persistence. Numerical simulations support our theoretical findings and provide further insights into the influence of key parameters on malaria transmission dynamics. These results contribute to a better understanding of malaria spread and inform the development of effective control strategies.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] D. Aldila, "Dynamical Analysis on a Malaria Model with Relapse Preventive Treatment and Saturated Fumigation," Computational and Mathematical Methods in Medicine, vol. 2022, 19 pages, 2022.

[2] R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Oxford University Press, Oxford, 1992.

[3] J. L. Aron, "Mathematical Modelling of Immunity to Malaria," Mathematical Biosciences, vol. 90, pp. 385-396, 1988.
Stability and sensitivity analysis of HIV Co-
Infections with HCV, HBV, and TB

**Communication Info**

**Authors:**

CHAIMAE EL MOURABIT¹

NADIA IDRISSI FATMI ¹

¹ LIPIM, National School of
Applied Sciences of Khouribga,
Sultan Moulay Slimane
University, Morocco

**Keywords:**

(1)HIV co-infections

(2) Mathematical modeling

(3) Stability analysis

**Abstract**

HIV co-infections with HCV, HBV, and TB pose challenges due to their complex interactions, immune effects, and treatment implications. This study develops a mathematical model using nonlinear differential equations to describe transmission dynamics and disease progression. The model incorporates viral replication, immune response, and treatments, including ART, DAAs for HCV, and anti-TB therapy. We analyze the stability of sub-models for HIV-HCV, HIV-HBV, and HIV-TB, deriving the basic reproduction number as a threshold for disease persistence. Stability conditions at disease-free and endemic equilibrium states are examined using the Jacobian matrix for local stability and Lyapunov functions for global stability. Furthermore, a sensitivity analysis is performed to assess the impact of key model parameters on the basic reproduction number and the equilibrium states. Numerical simulations are carried out to validate the theoretical findings.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Mostafavi, E., Ebrahimi, B., Doosti-Irani, A. and Mirzazadeh, A., 2024. Prevalence of hepatitis B, hepatitis C, and tuberculosis among people living with HIV in Iran: a systematic review and meta-analysis. BMC Infectious Diseases, 24(1), p.777.

[2] El Mourabit, C. and Idrissi Fatmi, N., 2024. Mathematical model analysis of hepatitis C with cardiac side effects before, during, and after receiving direct acting antivirals treatment. Commun. Math. Biol. Neurosci., 2024, pp.Article-ID.

[3] J.P. La Salle, The stability of dynamical systems, SIAM, Philadelphia, 1976.

[4] Teklu, S.W. and Workie, A.H., 2024. A dynamical optimal control theory and cost-effectiveness analyses of the HBV and HIV/AIDS co-infection model. Frontiers in Public Health, 12, p.1444911.

[5] J.K. Hale, Ordinary differential equations, Dover Publications, Mineola, 2009.
<figure><img src="image_39.png" /></figure>

Multi-cell discrete-time SIRI epidemic model
with travel restrictions and vaccination controls

**Communication Info**

**Authors:**

Samira ZOUHRI¹
Mohcine ELBAROUDI ¹
Hassan LAARABI¹

¹ Laboratory of Analysis,
Modeling, and Simulation
(LAMS), Department of
Mathematics and Computer
Science, Hassan II University of
Casablanca, Faculty of Sciences
Ben M'sik, Casablanca,
Morocco

**Keywords:**

(1) Discrete SIRI model

(2) multi-cell

(3) optimal control

**Abstract**

In this paper, we propose a multi-cell discrete-time SIRI epidemic model that describes the spatial-temporal spread of an infectious disease in a geographical domain represented as a grid of cells (regions) divided into $p^2$ cells. We assume that people can move between these cells due to their connectivity. To investigate the efficacy of travel restrictions and vaccination in preventing epidemic spread, we include two control variables in our model. We aim to reduce the number of infected individuals in each cell designated as infectious by the health authority, while also minimizing the expenses associated with implementing the travel ban and vaccination efforts. We develop an optimal control approach using the definition of a supplementary function that identifies the automatic activation of travel restrictions and vaccination in every cell according to health authority decisions. We present numerical results testing the spread of epidemics in different scenarios.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Lenhart, T. Workman, Optimal Control Applied to Biological Models. Chapman and Hall/CRC Mathematical and Computational Biology Series, 2007.

[2] W. Ding, R. Hendon, B. Cathey, E. Lancaster, R. Germick, Discrete time optimal control applied to pest control problems, Mathematical Sciences Publishers, 7(4), 2014, 479-489.

[3] O. Zakary, M. Rachik, I. Elmouki, On the analysis of a multi-regions discrete sir epidemic model: an optimal control approach, Int. J. Dyn. Control, 5 (3), 2017, 917-930.

[4] X. Tian, R. Xu, N. Bai, J. Lin, Bifurcation analysis of an age-structured SIRI epidemic model, Mathematical Biosciences and Engineering. 17(6), 2020, 7130-7150.

[5] M. McAsey, L. Mou, W. Han, Convergence of the forward-backward sweep method in optimal control, Comput Optim Appl, 53, 2012, 207-226.
Commutativity of prime rings and Banach
algebras with generalized (β, α)-derivations

**Communication Info**

**Author:**
Abderrahmane RAJI

LMACS Laboratory, FST, Sultan
Moulay Slimane University,
Beni Mellal, Morocco

**Keywords:**

(1) Prime rings

(2) Prime Banach algebras

(3) Generalized (β, α)-
derivations.

**Abstract**

In ring theory, numerous research in ring theory have
demonstrated that certain rings must be commutative
under certain conditions. In this context, we recall an
important result due to Howard E. Bell [3, Theorem
4.1], where he showed that a prime ring R with nonzero
center and char(R) = 0 or char(R) > n > 1 must be a
commutative ring if R admits a nonzero derivation d
satisfying d([xn, y]) - [x, yn] ∈ Z(R) for all x, y ∈ R.

Our major objective is here is to use this idea to
investigate the commutativity of prime associative rings
and prime Banach algebras with generalized (β, α)-
derivations satisfying certain differential identities.
Consequently, we use continuous linear generalized (β,
α)-derivations to extend our theoretical results on rings
to unital Banach algebras.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Ali and A. N. Khan, On commutativity of Banach algebras with derivations, Bulletin of the Australian Mathematical Society, 91(3) (2015), 419-425.

[2] M. Ashraf and B. A. Wani, On commutativity of rings and Banach algebras with generalized derivations, Advances in Pure and Applied Mathematics, 10(2) (2019), 155-163.

[3] H. E. Bell, On the commutativity of prime rings with derivation, Quaestiones Mathematicae, 22 (1999), 329-335.

[4] A. Boua, A. Raji and M. El hamdoui, Commutativity of prime rings and Banach algebras with generalized (β, α)-derivations, Palestine Journal of Mathematics, 13(4)(2024), 789-796.

[5] A. Boua, A. Raji and M. El hamdoui, Projection and commutativity of prime Banach algebras, Palestine Journal of Mathematics, 13(4)(2024), 1098-1104.
<figure><img src="image_40.png" /></figure>

Spectrum of discrete 2n-th order difference opereur with periodic
boundary conditions and its applications

Communication Info

Authors:

Omar Hammouti

Sidi Mohamed Ben Abdellah
University, Fez, Morocco

Keywords:

(1) discrete boundary value
problems

(2) 2n-th order

(3) variational methods

Abstract

Let n∈ N*, and N≥n be an integer. We study the
spectrum of discrete 2n-th order eigenvalue problems:

$$
\left\{
\begin{array}{l}
\displaystyle \sum_{k=0}^{n} (-1)^k \Delta^{2k} u(t-k) = \alpha u(t), \quad t \in [1, N]_{\mathbb{Z}}, \\
\\
\displaystyle \Delta^i u(-(n-1)) = \Delta^i u(N-(n-1)), \quad i \in [0, 2n-1]_{\mathbb{Z}}
\end{array}
\right.
$$

where α is a parameter, [1, N]z denotes the discrete
interval {1, 2, 3, ..., N} and Δ is the forward difference
operator defined by Δu(t)=u(t+1)-u(t), Δ⁰u(t)=u(t)

$$
\text{and } \Delta^i u(t) = \Delta^{i-1} (\Delta u(t)) \text{ for } i=1,2,3,\dots,2n.
$$

As an application of this spectrum results, we show the
existence of a solution of discrete nonlinear 2n-th order
problems by applying the variational methods and
critical point theory.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] A.R. El Amrouss and O. Hammouti, Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications. Opuscula Math., 41 (4) (2021), pp. 489-509.

[2] A.R. El Amrouss and O. Hammouti, Multiplicity of solutions for the discrete boundary value problem involving the p-Laplacian. Arab J. Math. Sci. (2021). DOI 10.1108/AJMS-02-2021-0050.

[3] A.R. El Amrouss and O. Hammouti, Existence of multiple solutions to a discrete 2n-th order periodic boundary value problem via variational method. Sci. Bulletin-Series A, 83 (3) (2021), pp. 159-170.

[4] John R. Graef, Lingju Kong and Min Wang, Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Discrete Contin. Dyn. Syst. suppl. (2013), 291-299.

[5] J. Zuo, O. Hammouti, S. Taarabti, Multiplicity of Solutions for Discrete 2n-TH Order Periodic Boundary Value Problem with φp-Laplacian, Axioms, 13(3) (2024), 1-15.
Integral inequalities for log (m; h1; h2) convex
stochastic

**Communication Info**

**Authors:**

Oualid Rholm<fnref n="1" />
Yassine Laarichi <fnref n="2" />
Mohammed Barmaki <fnref n="3" />

**Keywords:**

(1) Keyword1 Godunova-Levin interval-valued functions

(2) Keyword2 Stochastic process

(3) Keyword3 Hermite-Hadamard and Jensen-type inequalities

**Abstract**

Godunova-Levin interval-valued functions have attracted considerable attention in mathematical research due to their versatility and wide-ranging applications across diverse domains [1].

Originally formulated within deterministic contexts, these functions provide a robust framework for addressing uncertainty and imprecision. However, as contemporary mathematical investigations increasingly intersect with stochastic processes, the significance of studying stochastic processes becomes apparent.

Consequently, there emerges a pressing need to extend the applicability of Godunova-Levin functions into the realm of stochastic processes.

the key motivations driving this research is the exploration of novel interval Hermite-Hadamard and Jensen-type inequalities within the context of stochastic processes, as demonstrated in the subsequent references [2], [3] and [4]. These inequalities serve as fundamental tools in mathematical analysis, playing pivotal roles in theoretical developments and practical

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] W. Afzal, E.Y. Prosviryakov, S.M. El-Deeb and Y. Almalki, "Some New Estimates of Hermite-Hadamard, Ostrowski and Jensen-Type Inclusions for h-Convex Stochastic Process via Interval-Valued Functions". Symmetry, vol. 15, no. 831, (2023).

[2] O. Rholm, M. Barmaki and D. Gretete. Fractional Integral Inequalities of Hermite-Hadamard Type for P-convex and Quasi-Convex Stochastic Process, The Australian Journal of Mathematical Analysis and Applications, (2023) vol. 20, no. 10.

[3] O. Rholm, M. Barmaki and D. Gretete. Hermite-Hadamard Inequalities Type Using Fractional Integrals for MT-convex Stochastic Process, Malaysian Journal of Mathematical Sciences, (2023) vol. 17, pp.473-485.

[4] D. Kotrys, Hermite-Hadamard inequality for convex stochastic processes, Aequa-tiones mathematicae., 83, (2012), pp. 143-151.

<footnote n="1">¹ ENSA Kenitra, Morocco</footnote>

<footnote n="2">² ENSA Kenitra, Morocco</footnote>

<footnote n="3">³ ESEF Kenitra, Morocco</footnote>
Comparative Study of Information-Theoretic
Multi-Label Feature Selection

Communication Info

Authors:

Hasna CHAMLAL¹
Tayeb OUADERHMAN²
Mouhsin MESKAOUI ³

¹²³ *Computer Science and Systems Laboratory (LIS), Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco*

**Keywords:**

(1) Multi-label learning

(2) Feature selection

(3) Information theory

(4) Label relationships

Abstract

Multi-label feature selection (MLFS) is essential in high-dimensional data analysis for identifying discriminative features while effectively managing label dependencies. This study presents a comparative analysis of two state-of-the-art MLFS methods—LRFS and LSMFS—each addressing distinct aspects of label interactions.

LRFS [1] reduces label redundancy by categorizing labels into redundant and non-redundant groups, optimizing feature subsets to minimize informational overlap and enhance discriminative power. In contrast, LSMFS [2] extracts all supplementary information and the maximum supplementary information of features for each label from other labels, leveraging inter-label dependencies to enrich the feature selection process.

The comparative evaluation, conducted on benchmark multi-label datasets, employs metrics including Hamming Loss, Accuracy, and Macro-F1. Results indicate that LRFS is particularly effective in redundancy-prone environments, while LSMFS excels in scenarios where inter-label information is pivotal for improving classification performance. These complementary strategies highlight the nuanced trade-offs in MLFS design, suggesting that method selection should align with specific dataset characteristics.

Future work will focus on formulating a new feature relevance term based on label importance-weighted relevance and label-dependency redundancy, aiming to further enhance feature selection and multi-label classification performance.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] Ping Zhang, Guixia Liu, Wanfu Gao, Distinguishing two types of labels for multi-label feature selection, Knowledge-Based Systems, 113, 2016, 106-117.

[2] Ping Zhang, Guixia Liu, Wanfu Gao, Jiazhi Song, Multi-label feature selection considering label supplementation, Knowledge-Based Systems, 130, 2017, 85-96.
# Numerical Analysis of Air Pollution Dispersion
from Steady Single Point Emission Source

## Communication Info

**Authors:**

Ait Lhoussain Hamid¹
Younes Abouelhanoune¹

¹ ENSA Al-Hoceima,
Abdelmalek Essaadi University,
Tetouan, Morocco.

**Keywords:**

(1) Emission Source

(2) Dispersion

(3) Air pollution modeling

## Abstract

Dispersion models predict the spread of pollutants from sources such as industrial sources, vehicle emissions, or unattended spills of chemicals, and therefore support planning for emergencies. It will be undertaken here from a single point source, taking wind direction and speed, molecular diffusion, and convection into account. Atmospheric dispersion is affected by meteorological conditions, topography, and source characteristics. Computational methods in numerical simulations aid in the modeling of pollutant dispersion from a point source, considering wind information, topography, and emission distribution. Air quality and possible impacts are simulated to assess cost-effective pollution control and mitigation strategies.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Y. Abouelhanoune & M. El Jarroudi. Dispersion Model of Air Pollutant from Continuous Single Point Source. IJERT, Vol. 2 Issue 12, December 2013.

[2] B. Pulvirenti and al. Numerical simulation of air pollution mitigation by means of photocatalytic coatings in real-world street canyons. Building and Environment. V 186, 2020.

[3] A. Leelossy and al. Dispersion modeling of air pollutants in the atmosphere. Cent. Eur. J. Geosci. V 6(3), 257-278, 2014

[4] P. Oyjinda and Nopparat Pochai. Numerical Simulation of an Air Pollution Model on Industrial Areas by Considering the Influence of Multiple Point Sources. International Journal of Differential Equations Volume 2019.
Feedback stabilization of non-homogeneous semilinear
neutral systems with distributed delay

**Communication Info**

**Authors:**

Mohamed ERRAKI¹

Atmane EL HOUCH²

¹ Hassan 2 University,
Casablanca, Morocco

² Hassan 2 University,
Casablanca, Morocco

**Keywords:**

(1) Semilinear systems

(2) Non-homogeneous
systems

(3) Neutral systems

(4) Strong stabilization

(5) Distributed delay

**Abstract**

This paper addresses the stabilization problem for a class of non-homogeneous semilinear neutral systems with distributed delay, evolving on a real Hilbert space. Sufficient conditions in term of observation estimates are given to achieve the strong stabilization via bounded feedback control. Moreover, under an appropriate decomposition of the state space, we consider a feedback control that depends only on the state projection on a suitable subspace and guarantee the exponential stabilization in the bilinear case. Finally, we present examples and numerical simulations to illustrate the effectiveness of the obtained results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] El Houch, A., Erraki, M., & Attioui, A. (2024). Strong and exponential stabilization of nonhomogeneous bilinear time delay systems of neutral type, International Journal of Control.

[2] Hale, J.K., & Lunel, S.M.V., (2002). Strong stabilization of neutral functional differential equations, IMA Journal of Mathematical Control and Information, 19, 5–23.

[3] Adimy, M., & Ezzinbi, K. (2004). Existence and stability of solutions for a class of partial neutral functional differential equations. Hiroshima Mathematical Journal, 34(3), 251–294.
**Communication Info**

**Authors:**

Hasna MOUJANI¹

Abderrazak KASSIDI²

Ali EL MFADEL³

M'hamed ELOMARI⁴

¹,²,⁴ Laboratory LMACS,
Faculty of sciences and
techniques, Sultan Moulay
Slimane University, Beni
Mellal, Morocco.

³Superior School of
Technology, Sultan Moulay
Slimane University, Khenifra,
Morocco.

**Keywords:**

(1) Double phase operator

(2) Galerkin method

(3) Young measure

**Abstract**

This paper deals with the existence of weak solutions for a class of nonlinear Dirichlet boundary value systems driven by a double phase Laplacian-like operator. We establish the required result under some assumptions on the nonlinearity $f$ by relying on Musielak-Orlicz-Sobolev spaces, the Young measures method for managing weak convergence and the Galerkin approximation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Bahrouni, V.D. Radulescu, and D.D. Repovs, Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves, *Nonlinearity*, 32, 2019, 2481–2495.

[2] J.M. Ball, A version of the fundamental theorem for *Young measures*. 344, 1989, 207-215.

[3] N. Bourbaki, *Integration I* (S. Berberian, Trans.), Springer-Verlag, Berlin, Heidelberg, 2004.

[4] B.D. Calvert and C.P. Gupta, *Nonlinear elliptic boundary value problems in $L^1(p)$ spaces and sums of ranges of accretive operators*, *Nonlinear Analysis*, 2, 1978, 1-26.

[5] Z.C. Chen and T. Luo, *The eigenvalue problem of $p$-Laplacian-like equations*. Acta Mathematica Sinica, 46, 2003, 631-638.
K-frames in super Hilbert c\*-modules

**Communication Info**

**Authors:**

LFOUNOUNE ABDELLATIF<fnref n="1" />

ROUMAISSAE EL JAZZAR<fnref n="2" />

*Faculty of Sciences,*
*University of Ibn Tofail,*
*Kenitra, Morocco*

**Keywords:**

(1) K-frame

(2) super Hilbert C\*-modules

(3) duality

**Abstract**

In this talk, we explore the theory of K-frames in super Hilbert C\*-modules, extending frame theory from Hilbert spaces to the richer structure of Hilbert C\*-modules. We introduce the concept of super Hilbert modules as direct sums of Hilbert C\*-modules and develop a framework for defining and characterizing K-frames in this setting. Our main results provide new characterizations of K-frames, along with necessary and sufficient conditions for sequences in super Hilbert C\*-modules to form K-frames. Furthermore, we examine the relationships between K-frames, minimal frames, and orthonormal bases, presenting several theoretical propositions and illustrative examples. These findings contribute to a deeper understanding of operator theory and functional analysis in the context of C\*-algebras, with potential applications in quantum information theory and signal processing.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Ahmdi, A. Rahimi, *K-Orthonormal and K-Riesz Bases*, Sahand Commun. Math. Anal. (2020), 59-72. https://doi.org/10.22130/scma.2020.130958.827.

[2] N. Assila, H. Labrigui, A. Touri, M. Rossafi, Integral Operator Frames on Hilbert C\*-Modules, Ann. Univ. Ferrara 70 (2024), 1271-1284. https://doi.org/10.1007/s11565-024-00501-z.

[3] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser Boston, 2003. https://doi.org/10.1007/978-0-8176-8224-8.

[4] J.B. Conway, A Course in Operator Theory, American Mathematical Society, Providence, 2000.

[5] R.J. Duffin, A.C. Schaeffer, A Class of Nonharmonic Fourier Series, Trans. Amer. Math. Soc. 72 (1952), 341-366.

[6] L. Gavruta, Frames for Operators, Appl. Comput. Harmon. Anal. 32 (2012), 139-144. https://doi.org/10.1016/j.acha.2011.07.006.

[7] M. Ghiati, M. Rossafi, M. Mouniane, H. Labrigui, A. Touri, Controlled Continuous *-g-Frames in Hilbert C\*-Modules, J. Pseudo-Differ. Oper. Appl. 15 (2024), 2. https://doi.org/10.1007/s11868-023-00571-1.

[8] D. Han, D.R. Larson, Frames, Bases, and Group Representations, American Mathematical Society, Providence, 2000.

[9] W. Jing, Frames in Hilbert C\*-Modules, PhD Thesis, University of Central Florida, 2006. [10] I. Kaplansky, Modules Over Operator Algebras, Amer. J. Math. 75 (1953), 839-858. https://doi.org/10.2307/2372552.

[11] A. Karara, M. Rossafi, A. Touri, K-Biframes in Hilbert Spaces, J. Anal. (2024). https://doi.org/10.1007/s41478-024-00831-3.

[12] H. Massit, M. Rossafi, C. Park, Some Relations between Continuous Generalized Frames, Afr. Mat. 35 (2024), 12. https://doi.org/10.1007/s13370-023-01157-2.

[13] A. Najati, M. Mohammadi Saem, P. Gavru, Frames and Operators in Hilbert C\*-Modules, Oper. Matrices 10 (2016), 73-81. https://doi.org/10.7153/oam-10-06.

[14] M. Rashidi-Kouchi, Frames in Super Hilbert Modules, Sahand Commun. Math. Anal. 9 (2018), 129-142. https://doi.org/10.22130/scma.2018.23847.

<footnote n="1">¹ IBN TOFAIL, KENITRA, MOROCCO</footnote>

<footnote n="2">² IBN TOFAIL, KENITRA, MOROCCO</footnote>
Les fondements mathématiques de l'Analyse en
composantes principales normées et applications.

Communication Info

Authors:

Ayad EL BAZ

ENCG, EL Jadida, Maroc

Keywords:

(1) Analyse en composantes principales

(2) Mathématique

(3) ACPN

(4) Donnée

(5) Information

Abstract

Ce travail présentera les fondements mathématiques de
l'analyse en composantes principales normées (ACPN)
ainsi qu'une application de cette technique sur des
données financières.

Dans un premier temps, nous exposerons les bases de
l'algèbre linéaire les plus utiles pour mieux expliquer
l'ACPN d'un point de vue mathématique
L'ACP, en tant que technique d'analyse des données,
s'intéresse à l'extraction et au résumé des informations
contenues dans une grande base de données
concernant des individus et des variables.

Dans le cadre de ce travail, nous expliquerons comment
se fait le passage d'un espace des variables, considéré
comme espace vectoriel, de grande dimension à un
espace de faible dimension. Une telle réduction se
réalise avec une faible perte d'information. Dans un
second temps, ce travail présentera une application de
l'ACPN sur des données financières sous le logiciel SPSS.
Il évoquera également les interprétations des résultats
obtenus qui prennent en considération les points de vue
mathématique et financier.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] Bourouche, J. M. & Saporta, G. (1992), Analyse des données. Presse Universitaire de France, 5`ème édition.

[2] Bertier, P. & Bourouche, J. M. (1981), Analyse des données multidimensionnelles. Presse universitaire de France.

[3] Diday, E., Lemaire, J., Pouget, J., & Testu, F. (1982), 'Eléments d'analyse des données. Edition Dunod.

[4] Escofier, B. & Pagés, J. (2016), Analyses Factorielles Simples et Multiples: cours et études de cas. 5ème édition, Dunod.

[5] Foucart, T. (1997), L'analyse des données : mode d'emploi. Presses universitaires de Rennes
<figure><img src="image_41.png" /></figure>

# Existence of solutions of fractional equation with fractional integral boundary conditions

## Communication Info

**Author:**
Karima ALI KHELIL

Badji Mokhtar University,
Annaba, Algeria

**Keywords:**

(1) Fractional derivative

(2) Boundary value problem

(3) Krasnoselsky's theorem

## Abstract

In this work, we are interested in the study of the following boundary value problem [1]:

$$ egin{cases} D^{\alpha} w(s) = \varphi(s, w(s)), \quad s \in (0,1), \\ w(0) = 0, \\ w(1) = I^{\beta} w(1), \\ w'(1) = I^{\beta} w'(1) \end{cases} $$

where $\varphi: [0,1] \times \mathbb{R}_+ \rightarrow \mathbb{R}_+$ is a continuous positive function and $D^\alpha$ is the Caputo fractional derivative operator of order $\alpha$, $I^\beta$ is the Riemann-Liouville fractional integral operator of order $\beta$ such that $2 < \alpha \le 3$, $0 < \beta < 1$.

The main objective are to obtain conditions for the existence of solutions [2].

We present different conditions for the existence of solutions based on Arzela-Ascoli and Krasnoselskii theorems [3, 4, 5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] I. Podlubny, Fractional Differential Equations, Academic, New York, 1999.

[2] B. Ahmad, S. Sivasundaram, On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order. Appl. Math. Comput. 217, 2010, 480-487.

[3] A. Bragdi, A. Frioui and A. Guezane Lakoud, Existence of solutions for nonlinear fractional integro-differential equations. Adv Differ Equ., 418, 2020.

[4] Su X., Landong L. Existence of solution for boundary value problem of nonlinear fractional differential equation. Appl. Math. J. Chin. Univ. Ser. B., 22 (3), 2007, 291-298.

[5] Su., Zhang S. Solutions to boundary value problems for nonlinear differential equations of fractional order. Electron J. Differ. Equ., 26, 2009, 1-15.
Enhanced Qualitative Results for Nonlinear Integro-Differential
Equations of Higher Order

**Communication Info**

**Authors:**

Melek GÖZEN

¹ Department of Business
Administration
Faculty of Management
Van Yuzuncu Yil University
65080, Erciş -Van, Turkey

**Keywords:**

(1) Enhanced qualitative
results

(2) integro-differential
equation

(3) higher order

(4) stability

(5) boundedness

**Abstract**

The objective of this study is to establish new and
improved results on the stability and boundedness of
solutions to higher-order integro-differential equations.
The fundamental approach in the proofs involves
defining a suitable new Lyapunov function to establish
the novel results of this study. We provide two examples
to verify the results of this study. This article presents
novel results and significant contributions to the
qualitative theory of higher-order integro-differential
equations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Adeyanju, A. A.; Ademola, A. T.; Ogundare, B. S., On stability, boundedness and integrability of solutions of certain second order integro-differential equations with delay. Sarajevo J. Math. 17(30) (2021), no. 1, 61–77.

[2] Berezansky, L.; Domoshnitsky, A., On stability of a second order integro-differential equation. Nonlinear Dyn. Syst. Theory 19 (2019), no. 1-SI, 117–123.

[3] Tunç, Osman; Tunç, Cemil; Petruşel, Gabriela; Yao, Jen-Chih. On the Ulam stabilities of nonlinear integral equations and integro-differential equations. Math. Methods Appl. Sci. 47 (2024), no. 6, 4014–4028

[4] Tunç, Cemil, Osman Tunç, On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order Mathematics 10, no. 22: 4235, 2022.

[5] Yassine, Hassan, Stability of global bounded solutions to a nonautonomous nonlinear second order integro-differential equation. Z. Anal. Anwend. 37 (2018), no. 1, 83–99.
A constructive method for feedback stabilization of a
collection of stochastic nonlinear systems

**Communication Info**

**Authors:**

HananeHIMMI¹
Mohamed Oumoun²

¹Ensa, Cadi Ayad University,
Marrakech, Morocco

²Ensa, Cadi Ayad University,
Marrakech, Morocco

**Keywords:**

(1) Simultaneous stochastic
stabilization

(2) State feedback

(3) Stochastic control
Lyapunov function

**Abstract**

The simultaneous stabilization problem consists in finding a single controller which simultaneously stabilizes a finite collection of control system. The goal of this communication is to study the problem of simultaneous stabilization in probability, by state feedback, for a class of nonlinear stochastic systems whose drift and diffusion terms are dependent on the control. We extend some results proved by [1] for deterministic control systems to a collection of stochastic nonlinear systems for which classical methods are not applicable and the coefficients are only continuous and not necessary Lipchitz.

Under the assumption that a collection of stochastic control Lyapunov functions is known and based on the generalized stochastic Lyapunov theorem [2], we drive sufficient conditions for the simultaneous stabilization by a continuous state feedback controller.

This work generalizes the previous work [3] and is published in [4]. An illustrative example is given to verify the effectiveness of the result.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] J.L. Wu, Simultaneous stabilization for a collection of single-input non linear systems, IEEE trans. Autom. Control 50, (2005), pp. 328-337.

[2] F. Li and Y. Liu, Global stability and stabilization of more general stochastic nonlinear systems, Journal of Mathematical analysis and application (2014)

[3] A. Iggidr, M. Oumoun and M.O. Sauza, Continuous simultaneous stabilization of single-input nonlinear stochastic systems, Asian Journal of Control, (2021).

[4] H. Himmi and M. Oumoun, On the simultaneous stabilization of stochastic nonlinear systems, Asian Journal of Control, Vol 25, N° 2, (2022).
# Study on the Behavior of Net Asset Values of Diversified Mutual Funds

## Communication

**Authors:**

Zineb BELLACHE ¹

Hicham

EL BOUANANI ²

Market Analysis and
Economic Governance
Research Laboratory

(MAEGE).

University HASSAN II,
Casablanca, Morocco

**Keywords:**

(1) Mutual Funds

(2) Net Asset Value

(3) Financial Market
Analysis

## Abstract

This study examines the performance dynamics of diversified UCITS in Morocco, analyzing the relationships between fund performance, benchmark indices, and macroeconomic and geopolitical events. The analysis highlights the conservative portfolio management approach adopted by Moroccan funds, which prioritizes stability and capital preservation. While this strategy results in low volatility, it also limits global market opportunity capture due to dependence on the domestic economy (1).

The Capital Asset Pricing Model (CAPM) is used to evaluate the influence of interest rates, inflation, and exchange rate fluctuations on fund returns, aligning with recent studies on macroeconomic impacts in emerging markets (2). Findings reveal that interest rates negatively impact fund values, with beta coefficients around 0.5, indicating limited correlation with global markets. However, positive alphas suggest benchmark outperformance despite limitations in qualitative data on management decisions (3).

Drawing parallels with research on macroeconomic policies in developing countries (4), this study advocates for incorporating qualitative data and sentiment analysis to better understand the drivers of fund performance in Morocco's unique financial landscape. These findings align with recent studies on investment funds in emerging markets, which highlight their specific characteristics and challenges (5).

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] AMMC, 2023. Moroccan Capital Market Authority. [Online] Available at: https://www.ammc.ma/fr/publications/guide-pedagogique-comprendre-les-opcvm

[2] ASFIM, 2024. Association des Sociétés Financières et d'Investissement du Maroc. [Online] Available at: https://www.asfim.ma

[3] Bank Al-Maghrib, 2022. [Online] Available at: https://www.bkam.ma

[4] Cortes, F. & Sanfilippo, L., 2020. Do Multi-sector Bond Funds Pose Risks to Emerging Markets? IMF Working Paper. [Online] Available at: https://www.imf.org/~/media/Files/Publications/WP/2020/English/wpiea2020152-print-pdf.ashx

[5] Issr Journals, 2022. Emerging Market Mutual Funds: Characteristics and Challenges. International Journal of Advanced and Applied Sciences. [Online] Available at: https://issr-journals.org/links/papers.php?application=pdf&article=IJIAS-16-178-04&journal
ICRAMCS 2025

THE SEVENTH EDITION OF THE INTERNATIONAL CONFERENCE ON
RESEARCH IN APPLIED MATHEMATICS AND COMPUTER SCIENCE

April 24-25-26, 2025 | Marrakech, Morocco

<figure><img src="image_42.png" /></figure>

Entropy Solutions for Some Elliptic Unilateral Problems with Degenerate coercivity

Communication Info

Authors:

Brahim EL OMARI¹

Youssef HAJJI 2

Hassane HJIAJ³

Ismail JAMIAI⁴

¹ Abdelmalek Essaadi
University, Tétouan, Morocco

² Abdelmalek Essaadi
University, Tétouan, Morocco

³ Abdelmalek Essaadi
University, Tétouan, Morocco

⁴ Abdelmalek Essaadi
University, Tétouan, Morocco

Keywords:

(1) Entropy solutions

(2) Unilateral Problems

(3) Obstacle problems

Abstract

In this work, we consider the following elliptic
unilateral problems with degenerate coercivity whose
prototype is given by:

$$
\begin{align*}
& -\sum_{i=1}^{N} D^{i} a_{i}(x, u, \nabla u) + g(x, u, \nabla u) \\
& \qquad = f - \sum_{i=1}^{N} D^{i} \phi_{i}(x, u) \quad \text{in } \Omega
\end{align*}
$$

with $u = 0$ on $\partial\Omega$.

Where $\Omega$ is an open bounded set of $\mathbb{R}^N$ ($N \ge 2$), where the Carathéodory functions $a_i(x, s, \xi)$ verifying the degenerate condition, and the lower order term $g(x, s, \xi)$ verify only some growth condition, and the $f$ data is assumed to belong to $L^1(\Omega)$.

In this work we prove the existence of unilateral
entropy solutions for these equations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] T. Ahmedatt, A. Ahmed, H. Hjiaj and A. Touzani: Existence of renormalized solutions for some anisotropic quasilinear elliptic equations, Kragujevac Journal of Mathematics, Vol 44(4), pp 617-637, (2020).

[2] Y. Akdim, M. Belayachi, H. Hjiaj, M. Mekkour: Entropy solutions for some nonlinear and noncoercive unilateral elliptic problems. Rend. Circ. Mat. Palermo, II. Ser 69, 1373-1392, (2020).

[3] L.Aharouch and J. Benouna Exixtence and uniqueness of solutions of unilateral problems in Orlicz spaces, Nonlinear Anal., 72 (2010), 3553-3565

[4] L. Boccardo and T. Gallouët Nonlinear elliptic equations with right-hand side measures. Comm. Partial Differential Equations,17 (1992), 641-655.

[5] H. Ayadi: The obstacle problem for degenerate anisotropic elliptic equations with variable exponents and L1-data. J. Nonlinear Funct. Anal., 2021, 1-17, (2021).
Mathematical Model for Heroin Consumption Spread with
Stability Analysis and Control Strategies

**Communication Info**

**Authors:**

Khadija BENCHEIKH <fnref n="1" />

Zineb ELGHOUBARI <fnref n="2" />

Regragui TAKI <fnref n="3" />

**Keywords:**

(1) Basic reproduction number

(2) stability analysis

(3) optimal control strategies

**Abstract**

Heroin, an opioid derived from morphine, poses serious public health problems due to its addictive nature and harmful effects on the central nervous system. Assuming that heroin use follows a process that can be modeled in the same way as an infectious disease [1]. Mathematical modeling is used as a tool to understand and control heroin addiction [2]. It is, therefore, essential to calculate the basic reproduction number R_0[3], analyze the local and global stability of equilibrium points, and identify the most critical strategies through optimal control theory [4]. This approach will help determine how such epidemics can be controlled and ultimately eradicated from communities.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] White, Emma and Comiskey, Catherine, Heroin epidemics, treatment and ODE modelling, Mathematical biosciences, 2007, 208(1), 312—324.

[2] Martcheva, Maia. An introduction to mathematical epidemiology.2015, 61.

[3] Van den Driessche, Paul and Watmough, James, Further notes on the basic reproduction number, Mathematical epidemiology, 2008, 159--178.

[4] Memarbashi, Reza and Sorouri, Elahe.Modeling the effect of information transmission on the drug dynamic. The European Physical Journal Plus, 2020, 135(1), 1--20.,

<footnote n="1">¹ Chouaib Doukkali, Faculty of Sciences, Eljadida Morocco</footnote>

<footnote n="2">² Chouaib Doukkali, Faculty of Sciences, Eljadida, Morocco</footnote>

<footnote n="3">³ Chouaib Doukkali, Faculty of Sciences, Eljadida, Morocco</footnote>
Semigroup Dynamics of a Conformable Spatial PDE:
Chaos and Hypercyclicity

**Communication Info**

**Authors:**

Khadija ELKHALLOUFY¹
Manal MENCHIH ¹
Khalid HILAL¹
Ahmed KAJOUNI¹

¹USMS, Beni Mellal, Morocco.

**Keywords:**

(1) Chaos

(2) Hypercyclicity

(3) Conformable spatial PDE

**Abstract**

The aim of this study is to analyze the dynamics of an initial value problem associated with a conformable spatial partial differential equation [1] within the space of complex-valued continuous functions on [0, +∞), where functions vanish at infinity. First, we demonstrate that the solution generates a strongly continuous semigroup [5]. Next, we construct a quasiconjugacy between this solution and another semigroup defined on a conformable weighted function space [2, 3]. Under specific conditions, we demonstrate that the problem exhibits both hypercyclicity and chaos.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 2014, 65–70.

[2] Matsui, M., Takeo, F.: Chaotic semigroups generated by certain differential operators of order 1. SUT J. Math. 37, 2001, 51–67.

[3] Menchih, M., Hilal, K., Kajouni, A., Samei, M.: Chaotic dynamics of conformable maturity-structured cell population models. Qual. Theory Dyn. Syst, 23, 2024, 271.

[4] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences (1992).
Properties of ‘Kermack KcKendrick’ like models

**Communication Info**

**Authors:**

Hamidou A DIALLO<fnref n="1" />

Khalil EZZINBI<fnref n="1" />

Nisrine OUTADA<fnref n="1" />

Gauthier SALLET<fnref n="2" />

**Keywords:**

(1) Kermack–McKendrick

(2) Final size

(3) MultiGroup

**Abstract**

In this paper, we investigate the mathematical
properties of a 'Kermack–McKendrick' like model that
extends the classical Susceptible–Infected–Removed
(SIR) framework by incorporating multiple infected
classes as well as dedicated compartments for
hospitalized and Intensive Care Unit (ICU) cases. This
model, formulated under five hypotheses detailed later
in the paper, comprises 13 compartments. We prove
that every solution trajectory converges to a disease-
free equilibrium. Moreover, we compute the basic
reproduction number and show that the model admits a
first integral. We also establish a final size relation,
demonstrating that the final size $S_\infty$ is uniquely
determined for any value of $R_0$. Finally, we extend our
analysis to an age-stratified model, leading to a multi-
group framework.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Andronico, C. Tran Kiem, J. Paireau, T. Succo, P. Bosetti, N. Lefrancq, M. Nacher, F. Djossou, A. Sanna, C. Flamand, H. Salje, C. Rousseau and S. Cauchemez, Evaluating the impact of curfews and other measures on SARS-CoV-2 transmission in French Guiana. Nat Commun 12, 1634, 2021.

[2] H. Salje, C. Tran Kiem, N. Lefrancq, N. Courtejoie, P. Bosetti, J. Paireau, A. Andronico, N. Hozé, J. Richet, CL. Dubost, Y. Le Strat, J. Lessler, D. Levy-Bruhl, A. Fontanet, L. Opatowski, PY. Boelle and S. Cauchemez. Estimating the burden of SARS-CoV-2 in France. Science, 2020

[3] Magal, O.Seydi, G.Webb Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission, Mathematical Biosciences, Volume 301, 2018.

[4] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics - i, Proc. Royal Soc. London, 115, 1927, pp. 700–721.

<footnote n="1">¹ Université Cadi Ayyad LMDP,
Marrakech, Morocco</footnote>

<footnote n="2">² Université de Lorraine IECL
CNRS 7502, Metz, France</footnote>
Asymptotic almost periodicity of bounded solutions for some
partial functional differential equations with delay

**Communication Info**

**Authors:**

Thami AKRID<fnref n="1" />

Abdelhai ELAZZOUZI <fnref n="2" />

Aziz OUHINOU <fnref n="3" />

**Keywords:**

(1) differential equations with delay

(2) fractional power of an operator

(3) spectral decomposition

**Abstract**

We investigate the solution's behavior for abstract inhomogeneous partial functional differential equations (PFDEs) accordingly to an asymptotically almost periodic exogenous term. Here, the linear operator is made of a sectorial operator and a functional operator in the phase space with a domain.

Firstly, when the semigroup solution is hyperbolic, we establish that bounded solutions on $\mathbb{R}^+$ are asymptotically almost periodic. Moreover, necessary and sufficient conditions are provided for the initial condition to yield an asymptotically almost periodic solution.

Secondly, in the non-hyperbolic case, using certain ergodicity techniques, sufficient conditions are established to determine whether a bounded solution on $\mathbb{R}^+$ is asymptotically almost periodic.

The obtained theoretical results are applied to a partial differential equation involving spatial derivatives in the delayed term.

This work is a continuation and generalization of the works [2; 3; 4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] T. Akrid, A. Elazzouzi and A. Ouhinou. Asymptotic almost periodicity of bounded solutions for some partial functional differential equations with delay. *Discrete Contin. Dyn. Syst. Ser. S* 18 (2025), no. 1, 321--349.

[2] M. Adimy, A. Elazzouzi and K. Ezzinbi, Reduction principle and dynamic behaviors for a class of partial functional differential equations, *Nonlinear Anal.*, 71 (2009), 1709-1727.

[3] C. C. Travis and G. F. Webb, Existence, stability, and compactness in alpha norm for partial functional differential equations, *Trans. Amer. Math. Soc.*, 240 (1978), 129-143.

[4] W. Arendt and C. J. K. Batty, asymptotically almost periodic solutions of inhomogeneous Cauchy problems on the half-line, *Bull. London Math. Soc.*, 31 (1999), 291-304.

[5] C. Zhang, Integration of vector-valued pseudo-almost periodic functions, *Proc. Amer. Math. Soc.*, 121 (1994), 167-174.

<footnote n="1">¹ CRMEF, Marrakech, Morocco</footnote>

<footnote n="2">² University Sidi Mohamed Ben Abdellah, Taza, Morocco</footnote>

<footnote n="3">³ University of Sultan Moulay Slimane, Béni Mellal, Morocco</footnote>
<figure><img src="image_43.png" /></figure>

Numerical shape optimization process based on a new shape derivative
formula constrained by a semi-linear PDE

Communication Info

Authors:

Taib ANNOUAOUI
Abdelkrim CHAKIB
Ibrahim KHALIL

Applied Mathematics Team
(AMT), Faculty of Sciences and
Techniques, Sultan Moulay
Slimane University, B.P.523,
Beni Mellal, Morocco

Keywords:

(1) Shape optimization

(2) Semi-linear PDE

(3) Convex domains

(4) Shape derivative

(5) Support function

(6) Gradient algorithm

Abstract

This work is devoted to investigate the performance of a shape
optimization approach based on the new shape derivative
formula, involving support functions of convex domains,
established in [1], through a comparative numerical study with
the approach based on the Hadamard's shape derivative using
the deformation of domains by vector fields [3]. In this regard, let
us mention that the effectiveness of this new approach for
solving classical shape optimization problems constrained to
Laplace or Stokes linear state equation, has recently been proved
in [2]. So, we aim here to extend and perform this shape
optimization process for solving more general shape
optimization problem constrained to a semi-linear partial
differential equation (PDE) involving appropriate nonlinear
functions. To do that, we begin first by showing the existence of
an optimal shape for the considered shape optimization problem,
then we derive the shape sensitivity analysis using both the
Hadamard's and the new shape derivative approaches, under
some regularity assumptions on the nonlinear function. Finally,
we propose a numerical comparative study between two shape
optimization processes resulting from these shapes derivatives
approaches, for solving shape optimization problems of
minimizing quadratic cost functionals, constrained to various
semi-linear PDE, associated to appropriate nonlinear functions.
This showed once again the effectiveness and performance of the
new approach, in solving this kind of problems, in terms of the
accuracy on the solution and CPU time, compared to the classical
approach.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

1. Boulkhemair, A. and Chakib, A. On a shape derivative formula with respect to convex domains. *Journal of Convex Analysis*, 21, n° 1, 67-87(2014).

2. Chakib, A., Khalil, I. and Sadik, A. An Improved Numerical Approach for Solving Shape Optimization Problems on Convex Domains. *Numerical Algorithms* 96, (2024).

3. Henrot, A., Pierre, M. Variation et optimisation de formes. Une analyse géométrique. Mathematics and Applications, vol. 48, Springer, Berlin (2005).

4. Sturm, Kevin. On shape optimization with non-linear partial differential equations. *Technische Universitaet Berlin (Germany)* (2015).
Universal Approximation for Partial Differential Equations: Bridging
Theory and Practice with Physics-Informed Neural Networks

**Communication Info**

**Authors:**

Mohamed ALOUAT<fnref n="1" />
Hicham EL BOUJAoui <fnref n="1" />
Said Raghay <fnref n="2" />

**Keywords:**

(1) Universal approximation
theorem

(2) Partial differential
equations

(3) Artificial Neural networks

(4) PINNs

**Abstract**

The universal approximation theorem (UAT) has played a foundational role in understanding the expressive power of neural networks, originally proving that feedforward neural networks can approximate any continuous function on a compact domain. Over time, these results have been extended to more complex function spaces, including Sobolev spaces and distributions, bridging the gap between classical function approximation and the numerical solution of partial differential equations (PDEs).

These developments have deepened our understanding of the capability of artificial neural networks to approximate not only a scalar-valued functions but also solutions of partial differential equations with varying degrees of regularity. In this work, we analyze fundamental results on universal approximation theorems in the context of PDEs and consider their implications for neural network-based methods. We also highlight the role of Physics informed neural networks (PINNs) as a numerical approach for solving PDEs, illustrating their relevance through selected examples.

By bridging theoretical insights with empirical results, this study aims to evaluate the extent to which neural networks can serve as robust solvers for PDEs.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Cybenko, G. Approximation by superpositions of a sigmoidal function. *Math. Control Signal Systems* **2**, (1989) 303–314.

[2] Kurt Hornik, Approximation capabilities of multilayer feedforward networks, Neural Networks, Volume 4, (1991), 251-257.

[3] Dmitry Yarotsky, Error bounds for approximations with deep ReLU networks, Neural Networks, Volume 94. (2017), Pages 103-114.

[4] Gühring, Ingo & Kutyniok, Gitta & Petersen, Philipp. Error bounds for approximations with deep ReLU neural networks in $W^{S,p}$ norms. Analysis and Applications. (2019)

[5] Zuowei Shen, Haizhao Yang, Shijun Zhang, Optimal approximation rate of ReLU networks in terms of width and depth, Journal de Mathématiques Pures et Appliquées, Volume 157, (2022), Pages 101-135,

<footnote n="1">¹ Ibn Zohr university, Agadir,
Morocco</footnote>

<footnote n="2">² Cadi Ayad university,
Marrakech, Morocco</footnote>
<figure><img src="image_44.png" /></figure>

Couples System of Nonlinear Impulsive Hybrid Differential Equations
with Linear and Nonlinear Perturbations Involving \psi-Caputo
Fractional Derivative

**Communication Info**

**Authors:**

Fatima-Ezzahra Bourhim
Ali El Mfadel 2
M'hamed Elomari 3

¹ LMACS laboratory, FST Beni Mella-Morocco

² LMACS laboratory, FST Beni Mella-Morocco

³ LMACS laboratory, FST Beni Mella-Morocco

**Keywords:**

(1) Coupled systems

(2) Fractional Derivative

(3) Fixed point theorems

**Abstract**

In this work, we prove the existence and uniqueness of solutions to impulsive coupled system of nonlinear hybrid fractional differential equations involving \psi-Caputo fractional derivative of order \alpha \in (0,1) with linear and nonlinear perturbations. We prove our main results by applying the nonlinear alternative of Leray-Schauder type and Banach's fixed point theorem. As application, on example is included to show the applicability of our results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Almeida, R: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlinear Sci. Numer. Simul. 44, 2017, 460-481.

[2] M. Hannabou, M. Bouaouid and K. Hilal, Coupled System of Nonlinear Impulsive Hybrid Differential Equations With Linear And Nonlinear Perturbations, TWMS J. App And Eng. Math, 15, 2024, 1434-1450.

[3] H. Gu, Y. Zhou, B. Ahmad and A. Alsaedi, Integral solutions of fractional evolution equations with nondense domain, Electronic journal of differential equations, 145, 2017, 1-15.

[4] Z. Baitichea, C. Derbazia, M. Benchohrab: $\psi$-$\psi$-Caputo Fractional Differential Equations with Multi-point Boundary Conditions by Topological Results in Nonlinear Analysis 3, 167-178.
# Study of Mild Solutions for Fractional Differential Inclusions under Nonlocal Conditions Involving the \psi-Caputo Derivative

## Communication Info

**Authors:**

Mahacine MALOUH<fnref n="1" />

M'hamed ELOMARI²

Mohamed BOUAOID<fnref n="3" />

**Keywords:**

(1) fractional differential inclusions

(2) Hausdorff measure of noncompactness

(3) Hausdorff measure of noncompactness

## Abstract

This is concerned with the existence of mild solutions for \psi-fractional differential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using fractional calculus, Hausdorff measure of noncompactness, and the milticalued fixed point theorem.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Tingting Lian, Changfeng Xue and Shaozhong Deng, BoundaryValueProblems, 219, 2016.

[2] Sabatier, J, Agrawal, OP, Tenreiro Machado, JA: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007).

[3] Lakshmikantham, V, Vatsala, AS: Basic theory of fractional differential equations. Nonlinear Anal. TMA 69, 2677-2682 (2008).

[4] Wang, J, Zhou, Y: A class of fractional evolution equations and optimal controls. Nonlinear Anal., Real World Appl. 12, 262-272 (2011)

<footnote n="1">¹ University Sultan Moulay Slimane, Beni Mellal, Morocco</footnote>

<footnote n="1">¹ University Sultan Moulay Slimane, Beni Mellal, Morocco</footnote>

<footnote n="3">³ University Sultan Moulay Slimane, Beni Mellal, Morocco</footnote>
Controability analysis of Hilfer fractional stochastic pantograph differential equation with
fractional Brownian motion and Poisson noise

Communication Info

Authors:

Ayoub LOUAKAR<fnref n="1" />

Devaraj VIVEK<fnref n="2" />

Ahmed KAJOUNI³

Khalid HILAL⁴

Keywords:

(1) <u>Pantograph</u> equations

(2) <u>Stochastic</u> equations

(3) <u>Control</u> theory

Abstract

We discuss the existence and controllability of the Hilfer
fractional stochastic pantograph equation with fractional
Brownian motion and Poisson noise. The existence of a
mild solution to the proposed problem is proved and the
controllability of the control problem is established. The
results are obtained using fractional calculus theory,
semigroup theory, stochastic analysis, and fixed-point
theory under sufficient conditions. The theoretical findings
are validated through an example.

<footnote n="1">¹,³,⁴ LAMSC, Sultan Moulay Slimane University, Beni Mellal, Morocco.</footnote>

<footnote n="2">² Department of Mathematics, PSG College of Arts and Science, Coimbatore-641 014, India.</footnote>
# Optimal Embeddings and Interpolation:
Connecting Sobolev Spaces and Their Norms

## Communication Info

**Authors:**

Maarir Souad *¹
El Hadfi Youssef ¹

*¹ Laboratory LIPIM,
National School of Applied
Sciences, Khouribga, 25000,
Sultan Moulay Slimane
University, Morocco.

**Keywords:**

(1) Optimal Inequalities,

(2) Sup-Laplacian Operator,

(3) Non-diffusion Equation.

## Abstract

The Gagliardo–Nirenberg inequalities are interpolation inequalities that were independently established by Gagliardo and Nirenberg in the late 1950s. Recently, their ties to theoretical aspects of information theory and nonlinear diffusion equations have enabled researchers to derive optimal forms of these inequalities, identifying both the sharp constants and the explicit solutions for optimizers. In this note, we explore the key connections between Shannon-type entropies, diffusion equations, and a category of these inequalities, in light of these recent discoveries.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Li, J., & Ma, L. (2021). Extremals to new Gagliardo–Nirenberg inequality and ground states. Applied Mathematics Letters, 120, 107266.

[2] Nguyen, H. M., & Squassina, M. (2018). Fractional Caffarelli–Kohn–Nirenberg inequalities. Journal of Functional Analysis, 274(9), 2661-2672.

[3] Toscani, G. (2019). The information-theoretic meaning of Gagliardo–Nirenberg type inequalities. Rendiconti Lincei, 30(2), 237-253.
Numerical Simulation of Biphasic immiscible flow in porous media

**Communication Info**

**Authors:**

JAHID Oumayma,
ABOU EL HANOUNE Younes,
BOUJRAF Ahmed

Abdelmalk Essaadi University,
National School of applied
Sciences, Al Hoceima,
Morocco.

**Keywords:**

(1) Out-flow in porous media

(2) biphasic

(3) immiscible

(4) incompressible

(5) finite volume

**Abstract**

This study is about the numerical resolution of biphasic flow problem establishment of the biphasic, immiscible flow in porous area equations, while considering that the two phases are incompressible. It is about Darcy's equation coupled with mass conservation's equation. The used method is the finite volume of the IMPES type (Implicit in Pressure, Clarify in Saturation). We also proceed on the numerical resolution of the system. The simulation results demonstrate the influence of rock heterogeneity, saturation distribution, and mobility ratios on flow dynamics. The proposed numerical approach provides valuable insights into multiphase transport phenomena in porous media, aiding in optimizing recovery strategies.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] B. Amaziane, M. Ossmani, E. H. Quenjel, and Y. Zahraoui. Convergence of a cvfe finite volume scheme for nonisothermal immiscible incompressible two-phase flow in porous media. The SMAI Journal of computational mathematics, 10:263-304, 2024.

[2] Mustapha El Jarroudi, Souad Benleghrib, and Younes Abouelhanoune. A transport model for a nonaqueous-phase organic liquid in saturated porous media, 2018.

[3] Sinha, Santanu and Gjennestad, Magnus and Vassvik, Morten and Hansen, Alex. A Dynamic Network Simulator for Immiscible Two-Phase Flow in Porous Media, 2019.

[4] Seyed Ali Ghoreishian Amiri, Ehsan Taheri, and Arash Alimardani Lavasan. A hybrid finite element model for non-isothermal two-phase flow in deformable porous media, 2021.

[5] Zhe Li, Guillaume Oger, and David Le Touzé. A finite volume weno scheme for immiscible inviscid two-phase flows, 2020.
# Log-volatility Models for Modelling Financial Return Series in the Presence of Zeros: a Comparative Study

## Communication Info

**Authors:**

Abdeljalil SETTAR¹

Sara CHEGDAL ¹

¹ Faculté des Sciences et
Techniques, Université Hassan
2, Mohammedia, Morocco

**Keywords:**

(1) log-GARCH

(2) SV

(3) Kalman filter

## Abstract

In this work, we address the challenges posed by zero returns in both log-GARCH and stochastic volatility (SV) models, with a particular focus on their asymmetric variants. Building upon previous imputation techniques for handling zero returns, as discussed in [1,2,3], we propose a unified approach that enhances parameter estimation accuracy for both model classes. Specifically, we employ the Quasi-Maximum Likelihood (QML) estimation method, incorporating the Kalman filter for both the asymmetric log-GARCH and asymmetric SV models, to ensure robust parameter estimation even in the presence of zero returns. A comparative study is conducted on a set of financial return series containing zeros, examining the performance of the models in question using our proposed estimation method.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Francq C., Wintenberger O., Zakoian J.M. (2013) GARCH models without positivity constraints: Exponential or log GARCH?. J. Econom. 177(1): 34-46

[2] Sucarrat G., Escribano A. (2013) Unbiased QML estimation of log-GARCH models in the presence of zero returns.

[3] Settar A., Badaoui M. (2021) On the treatment of zero returns in the estimation of log-GARCH model: empirical study. IOP Conf. Ser.: Mater. Sci. Eng. IOP Publishing, p. 012029.
Mathematical Advances in 3D Numerical Analysis for Air Pollution Dispersion Models

**Communication Info**

**Authors:**

Mehdi FARHANE <fnref n="1" />

Abbes KADYRI <fnref n="1" />

Abdelilah KADDAR <fnref n="2" />

Otmane SOUHAR <fnref n="1" />

**Keywords:**

(1) Advection-Diffusion Model

(2) Logarithmic Wind Profile

(3) GILTT Method

(4) Numerical Analysis

(5) Atmospheric Dispersion

**Abstract**

Air pollution dispersion modeling is essential for understanding pollutant transport in the atmospheric boundary layer. This study presents mathematical advances in 3D numerical analysis applied to an advection-diffusion model, incorporating a logarithmic wind speed profile. This term prevents the derivation of an exact analytical solution in the general framework, thus requiring an advanced numerical approach. We employ the Generalized Integral Laplace Transform Technique (GILTT) to obtain a robust and physically consistent numerical solution. A rigorous validation is performed by comparing our results with experimental atmospheric dispersion data from Copenhagen and Prairie Grass. The excellent agreement observed between simulations and experimental measurements demonstrates the relevance of the proposed model and its potential for applications in air quality assessment and regulatory decision-making.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Farhane, M.; Souhar, O. Generalized 3D Model of Crosswind Concentrations and Deposition in the Atmospheric Boundary Layer. Atmosphere 2024, 15, 1054.

[2] Farhane, Mehdi, Omar Alehyane, and Otmane Souhar. "Three-dimensional analytical solution of the advection-diffusion equation for air pollution dispersion." The ANZIAM Journal 64.1 (2022): 40-53.

[3] Kadyri A., Kandoussi K., Souhar O., An approach on mathematical modeling of PV module with sensitivity analysis: a case study. Journal of Computational Electronics, (2022), 1365-1372.

<footnote n="1">¹ Chouaib Doukkali University,
El Jadida, Morocco</footnote>

<footnote n="2">² ENSA, El Jadida, Morocco</footnote>
Mathematical Analysis of a Stochastic Epidemic Model: Existence, Uniqueness, Persistence, and Control

**Communication Info**

**Authors:**

MOHAMED OUTAIK

**Affiliation:**

université chouaib doukkali
faculté des sciences el jadida

**Keywords:**

-Brownian Motion.

-Stochastic Perturbation.

- Existence and Uniqueness
(of Solutions).

-Persistence (of Disease).

-Stochastic Stability.

-Intervention Strategies.

**Abstract**

This study focuses on the mathematical analysis of an epidemic model. Starting from a classical deterministic formulation, we introduce a Brownian motion-type noise term to account for the inherent random fluctuations in population dynamics and disease transmission. The primary objective is to rigorously investigate the mathematical properties of this stochastic model. We establish results regarding the existence and uniqueness of strong solutions, thereby ensuring the well-definedness of the model. Particular attention is paid to the persistence of the disease, that is, its ability to persist within the population over the long term despite stochastic perturbations. We also analyze the stability of the system, exploring the conditions under which equilibria can be perturbed or reinforced by the noise. Finally, we address the question of epidemic control within the stochastic context. We investigate the impact of various intervention strategies on disease dynamics, taking into account the uncertainty introduced by the Brownian motion. The results obtained allow us to evaluate the robustness of these strategies in the face of random fluctuations and to propose recommendations for effective disease management.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Egonmwan, A., Okuonghae, D., Mathematical analysis of a tuberculosis model with imperfect vaccine, International Journal of Biomathematics, 12, 2019, 1950073.

[2] Joshi, H. R., Optimal control of an HIV immunology model, Optimal Control Applications and Methods, 23, 2002, 199–213.

[3] Koutou, O., Traoré, B., Sangaré, B., Mathematical modeling of malaria transmission global dynamics: Taking into account the immature stages of the vectors, Advances in Difference Equations, 2018, 1–34.

[4] Tesfay, A., Saeed, T., Zeb, A., Tesfay, D., Khalaf, A., Brannan, J., Dynamics of a stochastic COVID-19 epidemic model with jump-diffusion, Advances in Difference Equations, 2021, 228.

[5] Gutierrez, J. B., Galinski, M. R., Cantrell, S., Voit, E. O., From within-host dynamics to the epidemiology of infectious disease: Scientific overview and challenges, Mathematical Biosciences, 270, 2015, 143–155.

[6] Emvudu, Y., Bongor, D., Koïna, R., Mathematical analysis of HIV/AIDS stochastic dynamic models, Applied Mathematical Modelling, 40, 2016, 9131–9151.
New absorbing boundary conditions for the
Schrödinger equation

**Communication Info**

**Authors:**

Sabah Kaouri<fnref n="1" />
Mostafa Abounouh <fnref n="2" />
Hassan Al Moatassime <fnref n="2" />

**Keywords:**

(1) Absorbing boundary conditions

(2) Transparent boundary conditions

(3) Schrödinger equation

(4) Finite Difference method

**Abstract**

This paper focuses on deriving transparent boundary conditions for the one-dimensional time-dependent Schrödinger equation. These conditions enable the restriction of the original PDE, defined on an unbounded domain, to a finite interval, making it suitable for numerical simulations with less reflections. The primary objective of this work is to develop an appropriate discretization of these transparent boundary conditions in combination with a selected discretization scheme for the PD, typically Crank-Nicolson finite differences for the Schrödinger equation. The resulting discrete transparent boundary conditions ensure an unconditionally stable numerical scheme while completely eliminating reflections at the boundaries.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Abderrazak Chrifi, Mostafa Abounouh, and Hassan Al Moatassime, Discrete and Continuous Dynamical Systems - S, 18, 2025, 269-295.

[2] Jiwei Zhang, Zhenli Xu, and Xiaonan Wu, Phys. Rev. E, 78, 2008, 026709.

[3] Antoine Xavier, Arnold Anton, Besse Christophe, Ehrhardt Matthias, and Schädle Achim, Commun. Comput. Phys., 4, 2008, 729-796.

[4] Arnold Anton, Ehrhardt Matthias Maike Schulte, and Ivan Sofronov, Communications in Mathematical Sciences, 10, 2012, 889-916.

[5] Buyang Li, Jiwei Zhang, and Chunxiong Zheng, SIAM Journal on Scientific Computing, 40, 2018, A4083-A4104.

<footnote n="1">¹ EMSI, Marrakesh, Morocco</footnote>

<footnote n="2">² FST, Marrakesh, Morocco</footnote>
**Communication Info**

**Authors:**

Brahim Khaider¹

Amine Laghrib ¹

Aissam Hadri ²

Lekbir Afraites ¹

¹ EMI, Sultan Moulay Slimane
University, Beni Mellal, 25000,
Morocco

² LAB SIV, Ibnou Zohr
University, Agadir, 80000,
Morocco

**Keywords:**

(1) neural network

(2) processing image

(3) denoising

(4) optimization

**Abstract**

This paper primarily focuses on nonconvex and nonsmooth minimization problems that consist of three terms, with practical applications including image recovery. The optimization model under study includes a fidelity term and two regularization terms, with the main challenges arising from the nonsmooth neural network-based regularization. To address these challenges, we first adopt the separation of the three operators method introduced by Davis and Yin [1] (referred to as DYS). Subsequently, we propose an algorithm that integrates the Plug-and-Play (PnP) [2] framework and the Learnable Descent Algorithm (LDA) [3]. We tackle the non-smooth and non-convex minimization problem by employing Nesterov's smoothing technique and developing the convergence theory for the three-operator splitting algorithm. Finally, numerical experiments were conducted to evaluate the performance of the PnP-LDA-LS algorithm against several

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] F. Bian and X. Zhang. A three-operator splitting algorithm for nonconvex sparsity regularization. *SIAM Journal on Scientific Computing*, 43(4):A2809–A2839, 2021.

[2] S. H. Chan, X. Wang, and O. A. Elgendy. Plug-and-play admm for image restoration: Fixed-point convergence and applications. *IEEE Transactions on Computational Imaging*, 3(1):84–98, 2016.

[3] Y. Chen, H. Liu, X. Ye, and Q. Zhang. Learnable descent algorithm for nonsmooth nonconvex image reconstruction. *SIAM Journal on Imaging Sciences*, 14(4):1532–1564, 2021.
A generalization of the Nash equilibrium solution

**Communication Info**

**Authors:**

Saloua AMRANI ZERRIFI
Ahmed DOGHMI

INSEA, Rabat, Morocco

**Keywords:**

(1) Nash Equilibrium

(2) Generalization of the Nash
Equilibrium solution

(3) Multi-valued functions

**Abstract**

The Nash equilibrium is one of the most important concepts in game theory, particularly for non-cooperative games. In this paper, we present a generalization of the Nash equilibrium solution. We begin by examining the problem of Nash implementation, introducing the concept of freedom to compare two strategies through an algorithm that measures this freedom within a given set. This approach allows us to generalize the Nash equilibrium solution and identify the necessary and sufficient conditions under which a multi-valued social choice correspondence can be implemented in this generalized framework. This generalization of the Nash equilibrium enables players with different strategies to achieve optimal expected payoffs in various situations that were previously unattainable.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Maskin, E. (1999). Nash equilibrium and welfare optimality. *The Review of Economic Studies*, **66**(1), 23-38.

[2] Repullo, R. (1987). A simple proof of Maskin's theorem on Nash implementation. *Social Choice and Welfare*, **4**(1), 39-41.

[3] Sjöström, T. (1991). On the necessary and sufficient conditions for Nash implementation. *Social Choice and Welfare*, **8**(4), 333-340.

[4] Yamato, T. (1992). On Nash implementation of social choice correspondences. *Games and Economic behavior*, **4**(3), 484-492.

[5] Moore, J., & Repullo, R. (1990). Nash implementation: a full characterization. *Econometrica: Journal of the Econometric Society*, **1083-1099**.
**Communication Info**

**Authors:**

Messikh Chahrazed

**Keywords:**

(1) Timoshenko system

(2) Thermoelasticity of type III

(3) General decay.

**Abstract**

In this work, we consider a one-dimensional thermoelastic Timoshenko system with memory damping terms. In this system, heat conduction is governed by Green and Naghdi's type III theory.

Thermoelasticity has attracted significant interest since Dafermos's pioneering article was published in 1968. Since then, many works have studied the asymptotic behavior using various methods, such as the multiplier technique and semigroup theory. For more details, one can refer to [1,5]. Notably, Salim A. Messaoudi and Belkacem Said-Houari [5] established exponential stability through the energy method. Additionally, Fatori et al. [4] demonstrated that exponential stability holds if and only if the wave speeds associated with the hyperbolic part of the system are equal.

The objective of our work is to study the same problem introduced by Ghennam and Djebabla [3], but with a modification in the boundary conditions, replacing theirs with Dirichlet-Neumann conditions. We prove that the system exhibits a general decay rate, independent of the system's coefficients, thereby improving upon the above mentioned work.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Apalara, T.A., Messaoudi, S.A., and Al-Smail, J.H., A stability result for the vibrations given by the standard linear model with thermoelasticity of type III, *Applicable Analysis*, **97**(10),2018, 1688-1700.

[2] Djellali, F., Labidi, S., and Taallah, F., Existence and energy decay of a Bresse system with thermoelasticity of type III, *Zeitschrift f¨ur angewandte Mathematik und Physik*, **73**,2022, 3-25.

[3] Ghennam, K. and Djebabla, A., Energy decay result in a Timoshenko-type system of thermoelasticity of type III with weak damping, *Mathematical Methods in the Applied Sciences*, **10**, 2018, 3868-3884.

[4] Fatori, L.H., Mu˜noz Rivera, J.E., and Monteiro, R.N., Energy decay to Timoshenko's system with thermoelasticity of type III, *Asymptotic Analysis*, **86**, 2014, 227-247.

[5] Messaoudi, S.A. and Said-Houari, B. Energy decay in a Timoshenko-type system of thermoelasticity of type III, *Mathematical Methods in the Applied Sciences*, **348**(1),2008, 298-307.
**Communication Info**

**Authors:**

Ousmane CISSE<fnref n="1" />

Jean-Tosse DIATTA <fnref n="2" />

Clément MANGA<fnref n="3" />

Ibrahima SANE <fnref n="4" />

**Keywords:**

(1) Local time SDE,

(2) Homogenization, Large
deviation 2

(3) Wentzell Boundary
conditions 3

**Abstract**

In this paper, we consider a stochastic differential equation (SDE) driven by a Brownian motion and which depends on two small parameters ($\delta$ parameter of homogenization and $\varepsilon$ parameter of large deviation). The SDE moves in the domain $\bar{D} = D \cup \partial D$ under Wentzell boundary conditions. We show that the family of solutions satisfies a large deviation principle with a good rate function. This result is an extension of the work Alioune and al [2].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Baldi P., Large deviations for diffusions processes with homogenization applications, Annals of Probability, (19), (1991), 509--524.

[2] Coulibay A.; Diedhiou A.; Sane I., On a Skorokhod problem with small double limit, Afrika mathematika, (30), (2019), 5--9.

[3] Freidlin M.I., Sowers R.B., A comparison of homogenization and large deviations, with applications to wavefront propagation, Stochastic Processes Appl., (82), (1999), 23--32.

[4] Pilipenko A., An Introduction to stochastic Differential Equations with Reflection, Postdam University Press 2014, Volume, 2014, Pages.

[5] Sato, K., Tanaka, H., Local times on the boundary for multidimensional reflecting diffusion. Proc. Japan Acad. Ser. A Math. Sci., 38, (1962), 699-702.

<footnote n="1">¹ UASZ, Ziguinchor, Sénégal</footnote>

<footnote n="2">² UASZ, Ziguinchor, Sénégal</footnote>

<footnote n="3">³ UASZ, Ziguinchor, Sénégal</footnote>

<footnote n="4">⁴ UASZ, Ziguinchor, Sénégal</footnote>
Absolute convergence of Mellin transforms

**Communication Info**

**Authors:**

Othman TYR¹

¹ESEFA, Ibn Zohr university,
Agadir, Morocco

**Keywords:**

(1) Mellin transforms

(2) Lipschitz conditions

(3) Mellin convolutions

**Abstract**

The problem of the integrability of Mellin transforms is presented. Sufficient Lipschitz conditions are given to solve this problem. These results are inspired by well-known works of Titchmarsh in classical Fourier harmonic analysis (see [1]). Some results on the integrability of Mellin transforms of the Mellin convolutions are also given.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Titchmarsh, E.C., Introduction to the Theory of Fourier Integrals, Clarendon press, Oxford, 1937.

[2] P. L. Butzer, A. A. Kilbas and J. J. Trujillo, Mellin transform analysis and integration by parts for Hadamard-type fractional integrals, J. Math. Anal. Appl. 270 (2002), 1–15.
Existence and stability results of a thermoelastic
nonlinear shear beam

Communication Info

Authors:

My Driss AOURAGH¹
Mustapha EL BAZ²

¹EST Meknès, AFAA Group,
Moulay Ismail University of
Meknès, Morocco

²AM2CSI Group, MSISI
Laboratory, FST Errachidia,
Moulay Ismail University of
Meknès, Morocco

Keywords:

(1) Nonlinear shear beam

(2) Faedo-Galerkin method

(3) Stability exponential

(4) Numerical result

Abstract

In this work, we analyze the stabilization of a thermo-elastic nonlinear shear beam model with thermal dissipation.

First, in this work, we establish the well-
posedness of the problem by using the Faedo-
Galerkin method. Next, we prove that the energy of
the problem decays exponentially regardless of any
relationship between coefficients of the system by
using multiplier method, since the system has only
one wave speed.

Finally, we validate our theoretical results
findings through some numerical experiments,
utilizing a finite element scheme in space and both
implicit Euler and Crank-Nicolson methods in time.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] Afilal, M., Aouragh, M.D., Feng, B., Segaoui, M. and Soufyane, A., Exponential decay rate of a nonlinear suspension bridge model by a local distributed and boundary dampings. Nonlinear Anal. Real World Appl. 68, (2022) p 103711.

[2] Aouragh, M. D., Segaoui, M. and Soufyane, A., "Exponential stability and numerical computation for a nonlinear shear beam system." Acta Mechanica 235.4, (2024) pp 029-2040.

[3] Arosio, A., A geometrical nonlinear correction to the timoshenko beam equation. Nonlinear Anal. Theor. Methods Appl. 47(2), (2001) pp 729-740.

[4] Kirchhoff, G., Mechanik, Teubner, Leipzig, vol 3 (1883).

[5] Woinowsky-Krieger, S., The effect of axial force on the vibration of hinged bars. J. Appl. Mech. 17, (1950) pp 35-36.
<figure><img src="image_45.png" /></figure>

Simulation numérique de la diffusion d'un pollutant dans un
cours d'eau

**Communication Info**

**Authors:**

Cyr-Séraphin NGAMOUYIH
MOUSSATA¹
Randhall Rosnille MPEMBA
MASSAKA²

¹ Université Marien NGouabi,
Brazzaville, Congo

¹ Université Marien NGouabi,
Brazzaville, Congo<

**Keywords:**

(1) Methode pseudo-spectrale

(2) Schéma numérique hybride

(3) Diffusio d'un polluant

**Abstract**

Dans ce travail, nous présentons un schéma numérique hybride
qui combine la méthode des éléments finis et la méthode
pseudo spectrale pour l'approximation spatiale. Le but est de
produire un schéma stable et convergent malgré le manque de
régularité dans la solution exacte. Nous avons démontré
l'efficacité de cette approche numérique par l'étude du
phénomène de diffusion de polluants dans un cours d'eau. Ce
problème est un modèle de réaction-diffusion non linéaire
appliqué à la propagation d'une espèce polluante au sein d'un
domaine spatial, sous l'effet d'un champ de vitesse fluide
stationnaire et incompressible.

Le problème aux limites est formulé comme suit :

$$
\left\{
\begin{array}{l}
\displaystyle \frac{\partial C}{\partial t} - \Delta C + v \cdot \nabla C + F(C) = 0 \quad \text{dans } [0; T] \times \Omega \\[1em]
\displaystyle \frac{\partial C}{\partial t} = 0 \quad \text{sur } [0; T] \times \partial\Omega \\[1em]
C(0) = C_0 \quad \text{dans } \Omega
\end{array}
\right.
$$

Où C(t, x, y) est la concentration du polluant en un point (x, y)
à l'instant t, v est la vitesse du fluide et F(C) représente le
terme de réaction du polluant.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Babuska I., Szabo B. A. and Katz I. N., The p-version of the finite element method, SIAM J. Numer. Anal., 18, 515, 1981.

[2] Boyd J.P., Chebyshev and Fourier Spectral Methods, Springer, 2001.

[3] Dubiner M., Spectral methods on triangles and other domains, J. Sci. Comput., 6, 345, 1991.

[4] Sherwin S.J. and Karniadakis G.E., A new triangular and tetrahedral basis for high-order (hp) finite element methods, International of journal finite elements methods in Engineering, vol 38, 3775-3802, 1995.

[5] Trefethen L. N., Spectral methods in Matlab, SIAM, Philadelphia, 2000.
<figure><img src="image_46.png" /></figure>

# Estimating parameters of stochastic SI<sub>a</sub>I<sub>s</sub> model for HIV transmission using the ensemble Kalman filter

## Communication Info

**Authors:**

Youssef BELGRAOUI¹

Aziza BELMAATI¹

¹ LMCSA Laboratory, Faculty of Sciences and Technology, Hassan II University, Mohammed, Morocco

**Keywords:**

(1) Stochastic SI<sub>a</sub>I<sub>s</sub> epidemic model

(2) HIV/AIDS

(3) Ensemble Kalman filter

(4) Estimation parameters

## Abstract

Stochastic epidemic models play a crucial role in studying the spread of infectious diseases, with the stochastic SI<sub>a</sub>I<sub>s</sub> model being particularly relevant for HIV transmission dynamics. These models often contain unknown parameters that can affect the accuracy of predictions. Therefore, estimating these parameters is essential for improving their reliability.

The stochastic SI<sub>a</sub>I<sub>s</sub> model divides the population into three compartments: susceptible individuals (S), infected individuals without obvious clinical symptoms (I<sub>a</sub>), and infected individuals with obvious clinical symptoms who are tested for HIV and diagnosed (I<sub>s</sub>). This model, as presented in the article by Rao et al. [1], provides a framework for understanding disease dynamics, predicting outbreaks, and assessing intervention strategies.

In this study, we estimate a few parameters of the model and the transmission states of HIV by developing an ensemble Kalman filter (EnKF) based on the stochastic SI<sub>a</sub>I<sub>s</sub> epidemic model [2-4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] F. Rao, Y. Tan and X. Lian, Stochastic analysis of an HIV model with various infection stages. Advances in Continuous and Discrete Models, 2025(1), 2025, 1-26.

[2] G. Evensen, Sequential Data Assimilation with a Nonlinear Quasi-Geostrophic Model Using Monte Carlo Methods to Forecast Error Statistics, Journal of Geophysical Research, 99, 1994, 10143-10162.

[3] R. Ghostine, M. Gharamti, S. Hassrouny and I. Hoteit, An extended SEIR model with vaccination for forecasting the COVID-19 pandemic in Saudi Arabia using an ensemble Kalman filter, Mathematics, 9, 2021, 636.

[4] R. Lal, W. Huang and Z. Li, An application of the ensemble Kalman filter in epidemiological modelling, Plos one, 16, 2021, e0256227.
Dynamic Analysis of a Fractional S1S2IQR
Epidemic Model with Standard Incidence Rate

**Communication Info**

**Authors:**

Yassine BABRHOU¹
Khadija CHANNAN
Brahim EL BOUKARI
Khalid HILAL
Ahmed KAJOUNI

¹ Laboratory LMACS, Sultan Moulay Slimane University, Beni Mellal, Morocco

**Keywords:**

(1) $S_{\{1\}}S_{\{2\}}IQR$ epidemic model

(2) fractional order
differential equations

(3) basic reproduction
number

**Abstract**

We propose a fractional epidemic model $S_{\{1\}}S_{\{2\}}IQR$ with a standard incidence rate using the Caputo fractional-order derivative [1]. For our proposed model, the existence, uniqueness, non-negativity, and boundedness of the solution are established [2]. The model has two equilibrium points: disease-free equilibrium and endemic equilibrium, and by using the method of next generation matrix we compute the basic reproductive number $R_{\{0\}}$ that determines the extinction and the persistence of the infection [3]. Furthermore the global asymptotic stability of steady states is established by using suitable Lyapunov functionals and applying LaSalle's invariance principle [4].

Finally, to illustrate our results, we establish a
numerical simulations [5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Li, H. L., Zhang, L., Hu, C., Jiang, Y. L., \& Teng, Z. Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge, Journal of Applied Mathematics and Computing, 54, 2017, 435-449.

[2] Babrhou Yassine, Cherkaoui Fatima, El Boukari Brahim, Hilal Khalid and Kajouni Ahmed, Analysis and optimal control of a fractional-order SEAIR epidemic model with two-strains, Gulf Journal of Mathematics, 19, 2025, 251-284.

[3] Van den Driessche, Pauline and Watmough, James, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180(1-2), 2002, 29-48.

[4] Channan Khadija, Hilal Khalid and Kajouni Ahmed, The asymptotic stability of a fractional epidemiological model, International Journal of Nonlinear Analysis and Applications, 14, 2023, 35-43.

[5] Petráš, I., Fractional-order nonlinear systems: modeling, analysis and simulation, Springer Science \& Business Media, 2011.
# New generalization of the C-condition for $(\xi; \zeta)$ mappings in Cauchy problem conformable on modular metric spaces

**Communication Info**

**Authors:**

Fadwa Gholali¹

Lalla Saadia Chadli ¹

Hicham Moussa ¹

¹ Laboratory of Applied
Mathematics and Scientific
Computing, Sultan Moulay
Slimane University, Beni Mellal,
Morocco

**Keywords:**

(1) Fixed point theorem

(2) Modular metric space

(3) C-condition

(4) $(\xi; \zeta)$-mappings

(5) Cauchy problem
conformable

**Abstract**

In this paper, we introduce a novel generalization of the C-condition for $(\xi; \zeta)$ mappings within the framework of modular metric spaces [3]. This work extends the fixed point results known for such mappings in traditional metric spaces to the more general setting of modular spaces. Specifically, we examine the boundary value problem under the scope of conformable derivatives, demonstrating the existence and uniqueness of solutions within modular metric spaces [1,2]. Our study contributes to the broader mathematical understanding by addressing several key aspects. Firstly, we provide a comprehensive analysis of the generalized C-condition [3], offering new insights and extending its applicability. Secondly, we explore the theoretical underpinnings of conformable derivatives [4] and their role in boundary value problems, thereby enhancing the existing theoretical framework. The practical importance of our results is showcased through various applications, highlighting their relevance and potential impact in real-world scenarios. These applications not only demonstrate the utility of our theoretical findings but also underscore the versatility of modular metric spaces in addressing complex mathematical problems. Overall, our results significantly enrich, extend, and generalize several previously established findings in the literature, paving the way for future research in this area. We believe that this work will serve as a foundational reference for further investigations into fixed point theory, modular metric spaces, and their applications.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Chistyakov, Vyacheslav V., *Modular metric spaces, I: basic concepts*. ;Nonlinear Analysis: Theory, Methods & Applications 72.1 (2010): 1-14

[2] Chistyakov, Vyacheslav, *Metric Modular Spaces: Theory and Applications* ;Cham: Springer, 2015.

[3] Gupta, Vishal, Naveen Mani, and Naveen Sharma., *Fixed-point theorems for weak $(\psi, \beta)$-mappings satisfying generalized C-condition and its application to boundary value problem.* ;
Computational and Mathematical Methods 1.4 (2019): e1041.

[4] Khalil, Roshdi, et al., *A new definition of fractional derivative*. ; Journal of computational and applied mathematics 264 (2014): 65-70
# Existence of Solutions for a Class of Superlinear Anisotropic Robin Problems with Variable Exponent

## Communication Info

**Authors:**

AbdelRachid El Amrouss

Fouad kissi

## Ali El Mahraoui

**Keywords:**

(1) variable exponent

Lebesgue space

(2) Anisotropic space

(3) Robin elliptic problems

## Abstract

In this work we study the existence of solutions of a nonlinear anisotropic elliptic Robin problem. We set up that the problem admits a sequence of weak solutions and multiplicity results under suitable conditions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] M.M. Boureanu, F. Preda, Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions, Nonlinear Differ. Equ. Appl. 19 (2012), 235–251.

[2] A. El Amrouss, A. El Mahraoui, Infinitely many solutions for elliptic equation with variable exponent, Proyecciones journal of Mathematics, 40(2021), no. 5, 1071-1096.

[3] B. Kone, S. Ouaro, S. Traore, Weak solutions for anisotropic nonlinear elliptic equations with variable exponents, Electron. J. Differ. Equ. 2009 (2009), 1–11.

[4] D.E. Edmunds, J. Raksonik, Sobolev embedding with variable exponent, Studia Math, 143(2000), 267-293.

<footnote n="1">¹ FSO, University Med</footnote>

<footnote>1^er, Oujda, Morocco</footnote>

<footnote n="2">² FSO, University Med</footnote>

<footnote>1^er, Oujda, Morocco</footnote>

<footnote n="3">³FSTH, University AbdelMalek</footnote>

<footnote>Essaadi, Al-Hoceima, Morocco</footnote>
<figure><img src="image_47.png" /></figure>

A functional equation originated from the product in a cubic number field

**Communication Info**

**Authors:**

Aziz MOUZOUN¹

Driss ZEGLAMI ²

¹Department of Mathematics,
E.N.S.A.M, Moulay ISMAİL
University, Menkes,
MOROCCO.

²Department of Mathematics,
E.N.S.A.M, Moulay ISMAİL
University, Menkes,
MOROCCO.

**Keywords:**

(1) Functional equation

(2) Number theory

(3) Multiplicative function

(4) Semigroup and monoid

**Abstract**

Let $K$ be either $\mathbb{R}$ or $\mathbb{C}$ and $\alpha \in \mathbb{R}$. We determine the semigroup

solutions $f: \mathbb{R}^3 \to S$ of the following new parametric functional
equation :

$$
\begin{align*}
f(x_1x_2 + \alpha y_1z_2 + \alpha y_2z_1, x_1y_2 + x_2y_1 + \alpha z_1z_2, x_1z_2 + x_2z_1 + y_1y_2) \\
&= f(x_1, y_1, z_1)f(x_2, y_2, z_2),
\end{align*}
$$

for all $(x_1, y_1, z_1), (x_2, y_2, z_2), \in \mathbb{R}^3$.

which results from the product of two numbers in a cubic free field.

We equip $\mathbb{R}^3$ with a binary operation to show that the non-zero
solutions of this equation are monoid homomorphisms.

We then investigate our results to introduce and find the solutions of
d'Alembert's functional equations with endomorphisms.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] J. Aczél and J. Dhombres, *Functional equations in several variables*, Cambridge University Press (New York, 1989).

[2] L. R. Berrone, L. V. Dieulefait, A functional equation related to the product in a quadratic number field. Aequationes math. (2011), (1-2), 167-175.

[3] A. Mouzoun, D. Zeglami, M. Ayoubi, A functional equation originated from the product in a cubic number field, Mediterr. J. Math. (2021). 18, 191.

[4] H. Stetkær, *Functional equations on groups*, World Scientific Publishing Company, Singapore (2013).

[5] D. Zeglami, *Some functional equations related to number theory*, Acta Math. Hungarica, 149 (2016), no 2, 490-508.
Viral Diffusion-Dynamics Model with Cellular
Immune Response

**Communication Info**

**Authors:**

AICHA SABIQ <fnref n="1" />

SAMIR BOUJIJANE <fnref n="2" />

KHALIL EZZINBI <fnref n="1" />

**Keywords:**

Reaction-Diffusion

Viral Dynamics

Cellular immune response

**Abstract**

In this paper, we study the global dynamical behavior of a viral dynamics model that incorporates immune responses [1] and spatial diffusion [2]. The global stability of the model is analyzed in terms of two threshold parameters, the basic reproduction number $R_0$ [3] and the immune response reproduction number $R_1$ [1]. The obtained results signify that the infection dies out if $R_0 \le 1$ and persists if $R_0 > 1$. Numerical simulations are performed to support our theoretical findings and to illustrate the impact of spatial diffusion on the stability of the model.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Dhar, S. Samaddar, P. Bhattacharya, R. Upadhyay, Viral dynamic model with cellular immune response: A case study of HIV-1 infected humanized mice, Physica A, vol.524 (2019) 1-14.

[2] F.B. Wang, Y. Huang & X. Zou, Global dynamics of a PDE in-host viral model, Applicable Analysis, 2014.

[3] W. Wang, X.Q. Zhao, Basic reproduction numbers for reaction-diffusion epidemic models, SIAM J. Appl. Dyn. Syst.11 (2012) 1652-167.

<footnote n="1">¹ LMDP-FSSM-UCA, Marrakesh,
Morocco</footnote>

<footnote n="2">² CRSA-UM6P, Benguerir,
Morocco</footnote>
# Mathematical and Numerical Analysis of Chemotherapy Resistance in Tumors: Modeling Integrating Darwinian, Lamarckian, and Microvesicle-Mediated Mechanisms with the WENO5 Scheme

## Communication Info

**Authors:**

Mohammed EL HAMMANI¹

Sidi Mohamed DOUIRI ¹

Imad EL HARRAKI ²

¹ Mohammed V university,
Rabat, Morocco

² ENSMR, Rabat, Morocco

**Keywords:**

(1) Tumor modeling

(2) Chemotherapy resistance

(3) Fixed point

## Abstract

We develop a mathematical model to describe the dynamics of chemotherapy-sensitive and resistant tumor cells, incorporating three resistance mechanisms: Darwinian selection, Lamarckian induction, and microvesicle-mediated transfer. Using a fixed-point method, we establish existence and uniqueness, prove positivity and mass preservation, and analyze asymptotic behavior. Numerical simulations highlight the impact of microvesicle transfer and Lamarckian induction on resistance. Our findings suggest that targeting these mechanisms could improve chemotherapy efficacy, providing insights into tumor growth and resistance dynamics for better treatment strategies.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Lefebvre, G., Cornelis, F., Cumsille, P., Colin, T., Poignard, C., Saut, O., Spatial modelling of tumour drug resistance: the case of gist liver metastases. Mathematical medicine and biology, 34(2), 2017, 151–176.

[2] Colin, T., Michel, T., Poignard, C., Mathematical study and asymptotic analysis of a model for tumour drug resistance, [Research Report] RR-8784, Inria Bordeaux Sud-Ouest. 2015, 32 p.

[3] Álvarez-Arenas, A., Podolski-Renic, A., Belmonte-Beitia, J., Pesic, M., Calvo, G.F., Interplay of darwinian selection, lamarckian induction and microvesicle transfer on drug resistance in cancer, Scientific reports 9(1), 2019, 1–13.

[4] Brezis, H., Functional Analysis, Sobolev Spaces and Partial Differential Equations, 2, Springer, New York, 2011.

[5] Rehman, A., Aslam, R.D., Meraj, M., Qamar, S.: High order finite volume weighted essentially non-oscillatory scheme for solving the isentropic two-phase flow model. Results in Applied Mathematics 6, 10, (2021), 100155.
<figure><img src="image_48.png" /></figure>

# The impact of tracing, monitoring, and hospitalizing on epidemic dynamics: an application to Ebola

**Communication Info**

**Authors:**

Mohamed LADIB¹

Aziz OUHINOU¹

¹ University of Sultan Moulay Slimane, Beni Mellal, Morocco

**Keywords:**

(1) Mathematical Epidemiology

(2) Contact tracing

(3) Ordinary Differential Equations (ODEs)

**Abstract**

In this work, we study the ODE system proposed in [1] to model the contact tracing intervention. The effective reproduction number is expressed in two main cases using the next-generation approach described in [2], then reformulated in terms of measurable quantities. According to found expressions, and when contact tracing is perfectly executed, we derive conditions on the fraction of untraced cases to be hospitalized and the average infections caused by traced cases, to bring the effective reproduction number below unity. In parallel, the existence of equilibria and the stability of the DFE are investigated. Moreover, the model is fitted to data of the Ebola disease collected by WHO during the 2014-2016 outbreaks in West Africa. Finally, numerical simulations are provided to explore the effect of some key parameters on the effective reproduction number.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Browne, C., Gulbudak, H., Webb, G., Modeling contact tracing in outbreaks with application to ebola. Journal of Theoretical Biology, 384, 2015, 33-49.

[2] Driesshe, P., Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180, 2002, 29-48.
Neural Network Approach for Estimating Initial Conditions and
Parameters in ODE Models: Application to an SEIuIdR
Epidemiological Framework

**Communication Info**

**Authors:**

Ahmed SADIK¹

Amine LAGHRIBE²

Aziz OUHINOU¹

¹ University of Sultan Moulay Slimane, Faculty of Sciences and Techniques, Béni Mellal, Morocco

² University of Sultan Moulay Slimane, National School of Applied Sciences, Khouribga, Morocco.

**Keywords:**

(1) Optimisation

(2) Artificial Neural
Networks

(3) Calibration

(4) Inverse problem

[5] Epidemic

**Abstract**

In this study, we present an innovative approach for parameter identification and initial condition calibration in autonomous models governed by ordinary differential equations (ODEs), beginning from any initial time t0; The method is applied to autonomous epidemiological models, including the SEIuIdR frameworks, and utilizes neural networks to optimize the objective function. This approach distinguishes itself through its simplicity and efficiency, offering promising outcomes for epidemiological modeling.

**References**

[1] Who. https://covid19.who.int/WHO-COVID-19-global-data.csv. consulted on October 1, 2022.

[2] Julien Arino, Khalid El~Hail, Mohamed Khaladi, and Aziz Ouhinou. A model for the early covid-19 outbreak in china with case detection and behavioural change. Biomath, 11(2):2212207--2212207, 2022.

[3] Zhihua Liu, Pierre Magal, and Glenn Webb. Predicting the number of reported and unreported cases for the covid-19 epidemics in china, south korea, italy, france, germany and United Kingdom. Journal of theoretical biology}, 509:110501,

[4] Roseline~N Okereke, Olaniyi~S Maliki, and Ben~I Oruh.A novel method for solving ordinary differential equations withartificial neural networks. Applied Mathematics, 12(10):900--918, 2021.

[5] Kayode Oshinubi. Mathematical and statistical modeling of epidemic data application to the novel COVID-19 outbreak}. PhD thesis, Université Grenoble Alpes [2020-....], 2022.
**Communication Info**

**Authors:**

Fatima ISMAGUE¹

Lekbir AFRAITES¹

Abdelilah HAKIM²

Mohamed Srati¹

¹Sultan Moulay Slimane
University, Beni-Mellal,
Morocco

²Cadi Ayyad University,
Marrakech, Morocco

**Keywords:**

(1) Inverse problem

(2) Optimal control

(3) Stability

(4) Optimization techniques

**Abstract**

In this paper, we study the inverse problem of identifying the initial condition in a linear subdiffusion model from measurement data using the alternating direction multiplier method (ADMM). The linear sub-diffusion model involves a Caputo fractional derivative of order $\alpha \in (0, 1)$ in time. To address our model, we first examine the regularity of the solution for the direct problem. Then, we establish the existence of the optimal solution and prove the convexity of the considered cost function by using its first derivative. Finally, the efficiency and accuracy of the present method are illustrated by some numerical examples.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Tuan, Vu, Inverse problem for fractional diffusion equation, Fractional Calculus and Applied Analysis, 14, 2011, 31--55.

[2] Dou, FF and Hon, YC, Numerical computation for backward time-fractional diffusion equation, Engineering Analysis with Boundary Elements, 40, 2014, 138--146.

[3] Salehi Shayegan, AH and Zakeri, A, A numerical method for determining a quasi solution of a backward time-fractional diffusion equation, Inverse Problems in Science and Engineering, 26, 2018, 1130--1154.

[4] Wang, Sen and Zhou, Xian-Feng and Pang, Denghao and Jiang, Wei, Existence and uniqueness of weak solutions to a truncated system for a class of time-fractional reaction--diffusion--advection systems, Applied Mathematics Letters, 144, 2023, 108720.
Spectral properties of skew-adjacency matrices
in tournaments

**Communication Info**

**Authors:**

Soukaïna MAHZOUM¹
Abderrahim BOUSSAIRI²
Sara EZZAHIR³
Soufiane LAKHLIFI 4

¹LMFA, FSAC Hassan II
University of Casablanca,
Casablanca, Morocco

²LMFA, FSAC Hassan II
University of Casablanca,
Casablanca, Morocco

**Keywords:**

(1) Tournament

(2) Skew-adjacency matrix

(3) Skew-characteristic polynomial

(4) Determinant

**Abstract**

A tournament is a digraph in which every pair of vertices is jointed by exactly one arc. Let T be a tournament with n vertices $v_1, ..., v_n$. The skew-adjacency matrix of T is the n × n zero-diagonal matrix $S = [s_{ij}]$, such that $s_{ij}=1$ if $v_i$ dominates $v_j$ and $s_{ij} = -1$ if $v_j$ dominates $v_i$. It is well-known that the determinant of S is zero or a square of an odd integer. The skew-characteristic polynomial of T is the skew-characteristic polynomial of its skew-adjacency matrix. In this talk we characterize the class of tournaments T such that every principal submatrix of their skew-adjacency matrices has determinant at most 9 and we introduce the skew-characteristic polynomial of tournaments in this class.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] BABAI, László et CAMERON, Peter J. Automorphisms and Enumeration of Switching Classes of Tournaments. The electronic journal of combinatorics, 2000, vol. 7, no 1, p. R38.

[2] CAMERON, Peter J. Orbits of permutation groups on unordered sets. Journal of the London Mathematical Society, 1978, vol. 2, no 3, p. 410-414.

[3] DENG, Bo, LI, Xueliang, SHADER, Bryan, et al. On the maximum skew spectral radius and minimum skew energy of tournaments. Linear and Multilinear Algebra, 2018, vol. 66, no 7, p. 1434-1441.

[4] MCCARTHY, Clifford A. et BENJAMIN, Arthur T. Determinants of the tournaments. Mathematics Magazine, 1996, vol. 69, no 2, p. 133-135

[5] MOORHOUSE, G. Eric. Two-graphs and skew two-graphs infinite geometries. Linear Algebra and its Applications, 1995, vol. 226, p. 529-551.
# Transferts de fonds et cycles économiques au Maroc : une analyse empirique

## Communication Info

**Authors:**

Samir FARHI¹
Hicham EL BOUANANI¹

LMAEG, Hassan II University of
Casablanca, Casablanca,
Morocco

**Mots-clés :**

(1) Transferts de fonds

(2) Propriétés cycliques

(3) Maroc

(4) Hodrick-Prescott

(5) Fonctions de réponses
impulsionnelles

## Résumé

Les transferts de fonds constituent une source vitale de financement pour de nombreux pays en développement, en raison de leur volume croissant et de leur potentiel à contribuer à la croissance et au développement des pays d'origine. Le Maroc s'inscrit pleinement dans cette dynamique. En outre, grâce à leur nature cyclique, ces transferts peuvent également fonctionner comme une forme d'assurance privée pour les pays bénéficiaires. La compréhension de ces propriétés cycliques est essentielle pour les pays qui dépendent fortement de ces flux, car cela leur permet de réagir de manière appropriée aux variations des cycles économiques et permet d'anticiper leur réaction au moment de crise. Cette communication examine la cyclicité des transferts de fonds vers le Maroc en appliquant le filtre de Hodrick-Prescott à des données annuelles de 1980 à 2022. Elle s'appuie sur des modèles économétriques et des fonctions de réponses impulsionnelles afin d'analyser les interactions entre ces flux et les cycles économiques.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

BOUOIYOUR, J., SELMI, R., & MIFTAH, S. (2018). The impact of remittances on economic growth in Tunisia: A dynamic panel data approach. The Journal of Developing Areas, 52(2), 165-180.

HAMMA, I. E. (2015) : « Transferts de fonds dans les pays du Sud de la Méditerranée : une approche macro-économique de leurs déterminants et de leurs effets (thèse de doctorat) », Document de Travail, Université de Nice Sophia Antipolis.

HODRICK, R. J., & PRESCOTT, E. C. (1997). Postwar U.S. business cycles : An empirical investigation. Journal of Money, Credit and Banking, 29(1), 1-16.

MUGHAL, M. Y., & AHMED, J. (2014). Remittances and business cycles : Comparison of South Asian countries. International Economic Journal, 28(4), 513-541.

PADHAN, H., BEHERA, D. K., SAHU, S. K., & DASH, U. (2022). Examining the cyclical pattern of remittance flow, migrants stock, and income of 31 pairs of countries with India. Migration Letters, 19(6), 911-931.

RUIZ, I., & VARGAS-SILVA, C. (2014). Remittances and the business cycle : A reliable relationship? Journal of Ethnic and Migration Studies, 40(3), 45

VATSA, P., LIM, S., & BASNET, H. C. (2022). Analyzing cycles in remittances and foreign direct investment: Evidence from the Philippines. Review of Development Finance, 12(2), 10-17.
Handling High-Dimensional Mixed Data: A
Penalized Regression Framework with SCOPE
and Adaptive Encoding Strategies

**Communication Info**

**Authors:**

Ismail ARJDAL¹
Echarif EL HARFAOUI²

¹ Faculty of Sciences, Chouaïb Doukkali University, El Jadida, Morocco

**Keywords:**

(1) Multiple linear regression

(2) Mixed variables

(3) High dimension

(4) Ridge, Lasso

(5) Group Lasso

(6) ENET

(7) SCOPE

**Abstract**

This study explores multiple linear regression techniques for high-dimensional (p >> n) datasets with mixed variable types (nominal, ordinal, and continuous). Traditional regression methods face challenges like multicollinearity and variable selection, especially with categorical variables. To address these, we employ penalized regression methods (Lasso, ENET, and SCOPE) alongside tailored coding strategies (full disjunctive, cumulative, and score-based coding). Through a real case study, we compare encoding approaches, demonstrating the effectiveness of our methodology in enhancing model robustness and parsimony. Our findings highlight SCOPE advantages in handling high-dimensional mixed data, offering insights for researchers and practitioners.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Hoaglin, D. C. (1984). Summarizing shape numerically: The -and- distributions, Exploring data tables, trends, and shapes, (chap. 11). John Wiley & Sons.

[2] Gertheiss, J. et Tutz, G. (2010). Sparse modeling of categorial explanatory variables. The Annals of Applied Statistics, http://dx.doi.org/10.1214/10-AOAS355.

[3] T. Hastie, R. Tibshirani et J.H. Friedman: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer Series in Statistics. Springer, 2009. ISBN 9780387848846.

[4] Stokell, B. G., Shah, R. D., & Tibshirani, R. J. (2021). Modelling high dimensional categorical data using nonconvex fusion penalties. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 83(3), 579-611. https://doi.org/10.1111/rssb.12432.

[5] Azzalini, A. (2023). Ordinal Variable Encoding in Regression Models: The smof Approach. In Journal of Applied Statistics; 50(1), 34-50.
# On Supercyclicity of Linear Relations

**Communication Info**

**Authors:**

Ali Ech-Chakouri

Department of Mathematics.
Dhar El Mahraz Faculty of
Science, Sidi Mohamed Ben
Abdellah University, BO 1796
Fes-Atlas, 30003 Fez
Morocco.

**Keywords:**

(1) Supercyclic

(2) Super transitive

(3) Linear Relation

**Abstract**

In this work, we introduce the notions of supercyclicity and super transitivity for linear relations (multivalued linear operators) on an infinite-dimensional separable Banach space.

We provide examples and establish several properties of supercyclic multivalued linear operators. We also determine conditions under which TS is a supercyclic multivalued linear operator if and only if ST is a supercyclic multivalued linear operator. Moreover, we present various characterizations of supercyclic linear relations. Among these characterizations, we show the equivalence between supercyclic multivalued linear operator and super transitive multivalued linear operator. Finally, we provide criteria for determining the supercyclicity of multivalued linear operators.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] E. Abakumov, M. Boudabbous and Maher Mnif, On Hypercyclic of linear relations, Results Math, 73:137 (2018).

[2] T. Álvarez, Quasi-Fredholm and semi-B-Fredholm linear relations, Mediterr. J. Math, 14:22 (2017).

[3] M. Amouch and O. Benchiheb, Some versions of supercyclicity for a set of operators, Filomat 35:5, (2021), 1619–1627.

[4] M. Amouch, A. Ech-Chakouri and H. Zguitti, On the disk-cyclic linear relations, Mathematica Bohemica, (2024), 1-22, doi: 10.21136/mb.2024.0015-24.
<figure><img src="image_49.png" /></figure>

# Disjoint Topologically Recurrent Operators

**Communication Info**

**Authors:**

El Mostafa SADOUK¹

Otmane BENCHIHEB²

Mohamed AMOUCH³

¹ Faculty of science, Chouaib Doukkali University, Eljadida, Morocco.

² Faculty of science, Chouaib Doukkali University, Eljadida, Morocco.

³ Faculty of science, Chouaib Doukkali University, Eljadida, Morocco.

**Keywords:**

(1) Hypercyclic operator

(2) Disjoint hypercyclic operator

(3) Recurrent operator

**Abstract**

In this article, we will discuss and introduce the notion of disjoint topological recurrence for finitely many operators acting on a real or complex Fréchet space X. In addition, we characterize the disjoint topologically recurrent of finitely many different powers of weighted shifts, both in the unilateral and bilateral cases, acting on sequence spaces.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] F. Bayart, E. Matheron, Dynamics of linear operators. 2009; New York, NY, USA, Cambridge University Press, 2009.

[2] Bés, J., Peris, A.: Disjointness in hypercyclicity. J Math Anal Appl 2007; 336: 297-315.

[3] Cardeccia, R., Muro, S.: Multiple recurrence and hypercyclicity. Math. Scand., 128(3), 16 pages (2022).

[4] Costakis, G., Manoussos, A., Parissis, I.: Recurrent linear operators, Complex Analysis and Operator Theory 8 1601-1643 (2014).

[5] Grivaux, S.: Hypercyclic operators, mixing operators and the bounded steps problem, J. Operator Theory 54, 147-168 (2005).
# Comparison of Two Algorithms for the Finite Volume Method

## Communication Info

### Authors:

a Ayoub CHEDDOUR

b Mohammed KRICHE

a Abdelhai ELAZZOUZI

a Department of mathematics,
Sidi Mohamed Ben Abdellah
University, Mathematics and
data science laboratory FP
Taza, Morocco.

b Department of mathematics,
Mohammed V University,
Laboratory of Mathematics,
Statistics and Applications Rabat,
Morocco.

### Keywords:

Finite volume method

Numerical Simulation

## Abstract

The finite volume method has been extensively studied by many researchers and plays a crucial role in various fields, including engineering and medicine. It is particularly used for modeling fluid flows and optimizing fluxes in transport networks. Moreover, this method is recognized for its accuracy and reliability in complex numerical models [1,2].

In this study, we address the issue of redundancy in the algorithm by optimizing the flux calculation. Specifically, we compute the flux only once and then multiply it by an appropriate factor to obtain the second flux. Additionally, we enhance efficiency by looping over edges rather than triangles. This approach reduces computational cost while maintaining solution accuracy.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Dalila Loudyi, Roger Falconer & Binliang Lin (2015) Méthode des volumes finis et précision des modèles numériques des écoulements souterrains, La Houille Blanche, 101:2, 39-44, DOI: 10.1051/lhb/20150017

[2] Jasak H. (1996) Error analysis and estimation for the finite volume method with applications to fluid flows. PhD Thesis,
Numerical technique for solving tempered
variational problems

**Communication Info**

**Authors:**

S. Ounamane¹

L. Sadek²

B. Abouzaid¹

E. Sadek¹

¹ National School of Applied Sciences, Chouaib Doukkali University, El Jadida, Morocco;

² Department of Mathematics, Faculty of Sciences and Technology, Al-Hoceima, Abdelmalek Essaadi University, Morocco

**Keywords:**

(1) TCFD

(2) TFVP

(3) estimate the error

**Abstract**

In this talk, we present the extended truncated exponential method for solving tempered fractional variational problems (TFVPs) with integral constraints. The method leverages the extended truncated exponential function (ETEF) and the tempered fractional derivative to transform TFVPs into solvable algebraic systems. We derive the operational matrix of derivatives for the ETEF and apply it to approximate the solutions of TFVPs efficiently. The method demonstrates superior performance in terms of computational efficiency and accuracy compared to existing approaches. Several numerical examples validate the effectiveness of our method and we compared the results of our method with those of [1] and [2].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Almeida, R., \& Morgado, M. L. (2019). Analysis and numerical approximation of tempered fractional calculus of variations problems. Journal of Computational and Applied Mathematics, 361, 1-12.

[2] S. Pooseh, R. Almeida, D.F.M. Torres, Discrete direct methods in the fractional calculus of variations, Comput. Math. Appl. 66 (2013) 668-676. [3] Authors, Title Journal, Volume, Year, Pages.