<figure><img src="image_50.png" /></figure>

A study of a class of nonlinear double-phase parabolic
systems: An example from advances in reaction-diffusion
models (ARD)

**Communication Info**

**Authors:**

Adnane KADDIRI<fnref n="1" />
Ahmed JAMEA <fnref n="2" />
Abdelghali AMMAR ⁴
El mehdi HASSOUNE <fnref n="1" />

**Keywords:**

(1) Double phase problem

(2) Existence

(3) uniqueness

**Abstract**

In this paper we are interested in the existence and uniqueness questions of a class of nonlinear double phase parabolic problems under Dirichlet type boundary conditions with a nonlinear source term which satisfies the L1-data regularity, which models advances in reaction-diffusion phenomena (ARD). In the functional framework of Musielak-Orlicz spaces, we use the Rothe method and semi-discrification of Euler then our goal is achieved.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] V.V. Zhikov, S.M. Kozlov, O.A. Olnik, Homogenization of Differential Operators and Integral Functionals, Springer-Verlag, Berlin, 1994.

[2] C. Zhang: *Entropy solutions for nonlinear elliptic equations with variable exponents*. Electronic Journal of Differential Equations 2014 (92), (2014),1-14.

[3] V.V. Zhikov, Averaging of functionals of the calculus of variations and elasticity theory, Izv. Akad. Nauk SSSR, Ser. Mat. 50(4) (1986) 675-710.

[4] J. I. Diaz, F. De Thelin: *On a nonlinear parabolic problem arising in some models related to turbulent flows*. SIAM Journal on Mathematical Analysis 25, (1994), 1085-1111.

[5] M. Sanchon, J.M. Urbano: *Entropy solutions for the p(x)-Laplace equation*. Transactions of the American Mathematical Society 361 (12), (2009), 6387-6405.

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

<footnote n="2">² National School of Applied Sciences, University of Chouaib Doukkali, El Jadida, Morocco.</footnote>
<figure><img src="image_51.png" /></figure>

TPFA method for Two-dimensional Burgers'
equation

**Communication Info**

**Authors:**

Zaroual Bazirha¹

Lahcen Azrar ¹,²

¹ Research Center STIS, M2CS,
Department of Applied
Mathematics and Informatics,
ENSAM, Mohammed V
University, Rabat, Moroco.

²Department of Mechanical
Engineering, Faculty of
Engineering, King Abdulaziz
University, Jeddah, Saudi
Arabia

**Keywords:**

(1) TPFA

(2) Semi-implicit

(3) Super-convergence

(4) Burgers' equation

**Abstract**

This paper presents a methodological approach based
on the Two-Point Flux Approximation (TPFA) finite
volume method [1] for solving the two-dimensional
viscous Burgers' equation [2]. A semi-implicit
discretization is applied to the nonlinear viscous
Burgers' equation. The approach leverages the
simplicity of the TPFA method, while avoiding the need
to solve the nonlinear system arising from the nonlinear
term in the equation. The accuracy and efficiency of the
proposed numerical scheme are demonstrated through
several tests, where the chosen time step depends only
on the square of the spatial step size.

Super-convergence is observed for low Reynolds
numbers in both the discrete L² and L∞-norms.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Eymard, R., Gallouët, T., & Herbin, R., *Handbook of numerical analysis*, 7, 2000, 713-1018.

[2] Wang, Y., Navon, I. M., Wang, X., & Cheng, Y., *International Journal for Numerical Methods in Fluids*, **82**(12), 2016, 909-931.
# The continuous Mehler-Fock wavelet packets transform

## Communication Info

**Authors:**

Abdelaali DADES¹

Radouan DAHER ²

¹ Hassan II university, FSAC,
Casabalanca, Morocco

² Hassan II university, FSAC,
Casabalanca, Morocco

**Keywords:**

(1) Wavelet

(2) Mehler-Fock transform

(3) Scale discrete function

## Abstract

In this talk, the continuous Mehler-Fock wavelet packets is defined and studied. More precisely, Plancherel and reconstruction formulas are given for this transform. The Calderón reproducing formula is also proved.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Trimèche K, Generalized harmonic analysis and wavelet packets: an elementary treatment of theory and applications, Florida: CRC Press, 2001.

[2] Prasad A, Verma SK, Continuous wavelet transform associated with zero-order Mehler-Fock transform and its composition. Int J Wavelets Multiresolut Inf Process. 2018, 16:1850050.

[3] Tyr O, Dades A, Daher R, Wavelet packet analysis associated with the Weinstein operator on $Rd+1$, J Anal. 2022, 31(1):31-56.
# Efficient Splitting Method for the Korteweg-De Vries Equation

**Communication Info**

**Authors:**

Salaheddine MAAQOUL¹
Hassan BELHADJ¹

¹ Department of Mathematics,
Faculty of Sciences and
Techniques of Tangier;
Abdelmalek Essaadi University,
Morocco.

**Keywords:**

(1) Korteweg-De Vries equation.

(2) Splitting Method.

(3) Finite Difference Method.

**Abstract**

In this work, the splitting method is employed to compute numerical solutions of the Korteweg-De Vries equation. For many years, this approach has been widely used to solve complex problems, yielding highly satisfactory results. First, we separate the linear and nonlinear terms and solve each subproblem using the most suitable numerical methods. Then, we analyze the stability and investigate the consistency of the splitting method. The theoretical accuracy and efficiency of the method are validated through numerical test cases. The proposed method offers the advantages of high precision and excellent running time.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Koroche, K. Aliyi, and H. Muleta Chemeda. "Sixth-order compact finite difference method for solving KDV-Burger equation in the application of wave propagations." *Iranian Journal of Numerical Analysis and Optimization* 12.2 (2022): 277-300.

[2] Kong, Desong, Yufeng Xu, and Zhoushun Zheng. "A hybrid numerical method for the KdV equation by finite difference and sinc collocation method." *Applied Mathematics and Computation* 355 (2019): 61-72.

[3] Karczewska, Anna, and Piotr Rozmej. "Shallow water waves-extended Korteweg-de Vries equations." *Oficyna Wydawnicza Uniwersytetu Zielonogórskiego, Zielona Góra* (2018): 13-22.

[4] Blanes, Sergio, Fernando Casas, and Ander Murua. "Splitting methods for differential equations." *arXiv preprint arXiv:2401.01722* (2024).

[5] HANSEN, Eskil et OSTERMANN, Alexander. Exponential splitting for unbounded operators. Mathematics of computation, 2009, vol. 78, no 267, p. 1485-1496.
Study of Water Seepage in Al-Wahda Dam and Its Impact on the
Stability of the Earth Dam

Communication Info

Authors:

Borhan AL RABEEI¹
Fouzia KASSOU²
Abdessamad GHAFIRI³

¹ Dept. Of Civil Engineering,
Université Hassan II, Faculté
des Sciences de Ben Msik,
Casablanca, Morocco

² Dept. of Civil Engineering,
Ecole Hassania Des Travaux
Publics, Casablanca, Morocco

³ Dept. Of Civil Engineering,
Université Hassan II, Faculté
des Sciences de Ben Msik,
Casablanca, Morocco

Keywords:

(1) Earth dam

(2) stability

(3) python

Abstract

The study addresses the challenges of seepage through
earth dams, focusing on continuous flow issues in
porous media and slope stability analysis. [1].

The Monte Carlo method is employed to solve
continuous flow problems, with results compared to the
finite element method. [2].

Circular slices are analyzed to determine the factor of safety, and overall stability is evaluated using the Monte Carlo method, specifically the random walking approach. [3].

A Python program, based on the Bishop method, iteratively calculates the factor of safety against sliding, providing accurate and refined results. [4.5]. This technique proves valuable in seepage analysis, offering a robust tool for estimating hydraulic head in dam bodies. The study establishes theoretical foundations and provides practical application and comparative analysis with the finite element method, yielding meaningful conclusions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] Adamo, Nasrat, et al. "Dam safety problems related to seepage." *Journal of Earth Sciences and Geotechnical Engineering* 10.6 (2020): 191-239.

[2] Auvinet, G. "Étude des écoulements en milieux poreux par la méthode de Monte Carlo." *Revue française de géotechnique* 70 (1995): 15-24.

[3] Yao, Aijun, Zhizhou Tian, and Yongjun Jin. "Sliding surface searching method for slopes containing a potential weak structural surface." *Journal of Rock Mechanics and Geotechnical Engineering* 6.3 (2014): 275-279.

[4] Bishop, Alan W. "The use of the slip circle in the stability analysis of slopes." *Geotechnique* 5.1 (1955): 7-17.

[5] Lemenkova, Polina. "Generic Mapping Tools and Matplotlib Package of Python for Geospatial Data Analysis in Marine Geology." *International Journal of Environment and Geoinformatics* 6.3 (2019): 225-237.
# On cotangent fractional operators and their properties

**Communication Info**

**Authors:**

Lakhlifa Sadek¹

¹ Department of
Mathematics, Faculty of
Sciences and Technology, BP
34. Ajdir 32003 Al-Hoceima,
Abdelmalek Essaadi
University, Tetouan,
Morocco

**Keywords:**

(1) Cotangent fractional integral;

(2) Cotangent fractional derivative

(3) Riemann-Liouville cotangent fractional derivative

(4) Caputo cotangent fractional derivative

**Abstract**

In this work, we present a new type of fractional derivatives involving exponential cotangent function in their kernels called Riemann-Liouville and Caputo cotangent fractional derivatives, respectively, and their corresponding integral. The advantage of the new fractional derivatives is that they achieve a semi-group property. We give some theorems and lemmas, and we give solutions to linear cotangent fractional differential equations using the Laplace transform.

© 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. 2014, 264, 65-70.

[2] Anderson, D.R. Second-order self-adjoint differential equations using a proportional-derivative controller. Comm. Appl. Nonlinear Anal. 2017, 24, 17-48.
<figure><img src="image_52.png" /></figure>

About the class of bounded-$E^a$ operators

**Communication Info**

**Authors:**

HOUDA MOKTAFI¹

HASSAN KHABAOUI²

KAMAL EL FAHRI³

¹ Ibnou Zohr University, Agadir,
Morocco

² Moulay Ismail University,
Meknès, Morocco

³ Ibnou Zohr University, Agadir,
Morocco

**Keywords:**

(1) Banach lattice.

(2) bounded-$E^a$ operator.

(3) L-weakly compact set.

**Abstract**

We introduce and study the class of the bounded-$E^a$ operators, which maps the closed unit ball of a Banach space to a subset of the maximal ideal $E^a$. Using the uaw-convergence and the un-convergence, we establish some equivalent conditions so that the range of a norm bounded set by an operator be a subset included in $E^a$. We extract in the sequel some important characterizations of bounded-$E^a$ operators. We provide as well some characterizations of the order continuity of the norm as an application. We examine the domination problem of this operator and provide the relation between the bounded-$E^a$ and the compact operators.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] C.D. Aliprantis and O. Burkinshaw, Positive operators. Springer, Berlin, 2006.

[2] O.Zabeti, Unbounded absolute weak convergence in Banach lattices, Positivity, 22, 2018, 501-505.

[3] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer-Verlag, Berlin, 1991.

[4] M. Kandić, H. Li, V. G. Troitsky, Unbounded norm topology beyond normed lattices, Positivity 22, 2018, 745–760.

[5] Y. Deng, M. O'Brien, and V.G. Troitsky, Unbounded norm convergence in Banach lattices, Positivity, 21, 2017, 963–974.
Network Scale Effects on Stochastic SIS Epidemic
Persistence and Extinction

Communication Info

**Authors:**

Bilal El Khatib¹

Adel Settati²

Aadil Lahrouz 3,4

1, 2, 3 Laboratory of
Mathematics and Applications,
Department of Mathematics,
Faculty of Sciences and
Techniques, B.P. 416-Tanger
Principale, Tanger, Morocco.

**Keywords:**

(1) White noise

(2) Stochastic epidemic model

(3) Extinction of disease

(4) Stochastic Persistence

(5) Complexe network

Abstract

This paper examines a stochastic SIS epidemic
framework on scale-free networks modeling human
contact patterns. Using white noise perturbation
techniques [1], we identify a threshold parameter
$R\sigma\delta$ that determines disease dynamics.
When $R\sigma\delta < 1$, infection exponentially
declines to extinction [3]; when $R\sigma\delta > 1$, the
disease persists stochastically. We analyze the
critical case of $R\sigma\delta = 1$ using techniques
from stochastic differential equations [2]. Our
research highlights how network structural
properties influence epidemic behavior, extending
time-delay approaches [4]. Computational
simulations incorporating scale-free network
topology provide comprehensive understanding of
the model's behavior, with implications for public
health policies and epidemic management
strategies based on stochastic population dynamics
[5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] X. Mao, G. Marion, E. Renshaw, Environmental Brownian noise suppresses explosions in population dynamics, Stochastic Process. Appl. 97 (2002) 95-110.

[2] J. Bao, B. Böttcher, X. Mao, C. Yuan, *Convergence rate of numerical solutions to SFDEs with jumps*, J. Comput. Appl. Math. 236 (2011) 119-131.

[3] J. Bao, C. Yuan, *Stochastic population dynamics driven by Lévy noise*, J. Math. Anal. Appl. 391 (2012) 363-375.

[4] J. Bao, X. Mao, G. Yin, C. Yuan, *Competitive Lotka-Volterra population dynamics with jumps*, Nonl. Anal. 74 (2011) 6601-16.

[5] E. Beretta, Y. Takeuchi, *Global stability of a SIR epidemic model with time delay*, J. Math. Biol. 33 (1995) 250-260.
# Numerical Analysis and Energy Decay of Timoshenko Linear Beam System

**Communication Info**

**Authors:**

Ali SMOUK ¹

Atika RADID ¹

¹ Faculty of Sciences Aïn Chock,
Hassan II University,
Casablanca Morocco

**Keywords:**

(1) Timoshenko linear beam

(2) Numerical approximation

(3) Energy decay

**Abstract**

This paper presents a comprehensive study of the Timoshenko linear beam model, focusing on the numerical approximation and energy decay properties of the system. We consider a system of partial differential equations that describe the dynamics of a Timoshenko beam, incorporating mass, inertia, and damping effects. The model is subject to clamped and free boundary conditions, and initial conditions are specified. We propose a finite element method combined with an implicit Euler scheme to approximate the solution of the system. The discrete energy associated with the numerical scheme is analyzed, and we prove that it decays over time under certain conditions. Numerical simulations are conducted to validate the theoretical results, demonstrating the effectiveness of the proposed method in capturing the energy decay behavior of the Timoshenko beam.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Akil, M., Dell'Oro, F., Fragnelli, G., Régnier, V., Soufyane, A. "Asymptotic behavior of the equivalent Timoshenko linear beam model used in the analysis of tower buildings." Zeitschrift für angewandte Mathematik und Physik, 76, 2025.

[2] Aouadi, M., Campo, M., Copetti, M.I.M., et al. "Existence, stability and numerical results for a Timoshenko beam with thermodiffusion effects." Z. Angew. Math. Phys., 70, 2019, 117.

[3] Messaoudi, S. A., Mustafa, M. I. "On the Internal and Boundary Stabilization of Timoshenko Beams." Nonlinear Differ. Equ. Appl., 15, 2008, 655-671.

[4] Piccardo, G., Tubino, F., Luongo, A. "Equivalent Timoshenko linear beam model for the static and dynamic analysis of tower buildings." Appl. Math. Modelling, 71, 2019, 77-95.
On the stability of a stochastic delay differential equations of fourth order

**Communication Info**

**Authors:**

Cemil TUNÇ¹
Zozan OKTAN²

¹,² Van Yuzuncu Yil
University, Van - Turkey

**Keywords:**

(1) Stability

(2) Stochastic differential equation,

(3) Lyapunov-Krasovskii functional,

(1) Variable time delay

**Abstract**

This article deals with a nonlinear stochastic differential equation of fourth order with variable time delays. In the article, a result on the asymptotic stability of zero solution of the considered equation is established. The proof of the result is based on the Lyapunov-Krasovskii functional method. To illustrate the verification of the result, an example is provided in a particular case. The result of the article extends and improves previous ones in the relevant literature.

**References**

[1] Abou-El-Ela, A. M.A. et al., On the stochastic stability and boundedness of solutions for stochastic delay differential equation of the second order, Chin. J. Math. (2015), Art. ID 358936, 8 PP.

[2] Tunç, Cemil; Oktan, Zozan, Improved new qualitative results on stochastic delay differential equations of second order. Comput. Methods Differ. Equ. **12** (2024), no. 1, 67–76.

[3] Tunç, Cemil; Oktan, Zozan, Stability and boundedness of stochastic integro-delay differential equations. J. Math. Anal. **15** (2024), no. 5, 69-83.

[4] Yuan-Hong, Yu; Wen-Deng, Cheng, On the boundedness and the stability properties of solution of certain fourth order differential equations. Applied Mathematics and Mechanics, 1990, 11: 881-887.

[5] Mao, Xuerong, Stochastic differential equations and applications. Elsevier, 2007.
Multiresolution analysis for solving viscoelastic
fluid flow with slip boundary conditions

**Communication Info**

**Authors:**

Meryieme EL Farragui¹

Otmane Souhar¹

Georgios C. Georgiou²

¹Department of Mathematics,
University Chouaib Doukkali, El
Jadida, Morocco

²Department of Mathematics
and Statistics, University of
Cyprus, Nicosia, Cyprus

**Keywords:**

(1) Johnson-Seglman model;

(2) Simple shear flow

(3) Navier slip

**Abstract**

The problem of Poiseuille flow involving a
Johnson-Segalman fluid [1] has been analyzed
analytically using the wavelet homotopy analysis
method (WHAM) [2, 3]. Initially, the
transformation of non-linear partial differential
equations into ordinary differential equations is
achieved, accounting for slip boundary conditions.
The resulting analytical solution is expressed as an
infinite series, and its convergence is established.
The evolution of the flow is studied in both the
stable and unstable regimes. We investigate the
impact of the slip numbers on the velocity profiles.
These results are consistent with existing research
on other Non-Newtonian flows with wall slip

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Georgiou, G. C., Vlassopoulos, D, (1998). On the stability of the simple shear flow of a Johnson-Segalman fluid. Journal of Non-Newtonian Fluid Mechanics, 75(1), 77-97.

[2] Liao, S. Beyond Perturbation: Introduction to Homotopy Analysis Methode, Chapman and Hall/CRC Press, Boca Raton, 2003.

[3] Liao, S. On the homotopy analysis methode for nonlinear problems, Applied Mathematics and Computation 147 (2) (2004) 499-513. https://doi.org/10.1016/S0096-3003(02)00790-7
<figure><img src="image_53.png" /></figure>

# Mathematical Modeling and Analysis of Fast Food Consumption Dynamics

**Communication Info**

**Authors:**

Issam Sahib¹

Bouchaib Khajji²

Mohamed Belam¹

¹ Laboratory LMACS, Sultan Moulay Slimane University, Department of Mathematics and Computer Science, Khouribga Polydisciplinary Faculty, Morocco

² Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University of Casablanca

**Keywords:**

(1) Mathematical Model

(2) Optimal Control

(3) Fast Food

**Abstract**

This research presents a continuous mathematical model, called PLSCQ, aimed at simulating the behavior of fast-food consumers influenced by public and private addiction treatment centers. The analysis focuses on the model's key features, including the basic reproduction number $R_0$, which assesses the potential spread of fast-food addiction within a population. A sensitivity analysis highlights the parameters with the most significant impact on $R_0$. Stability analysis shows that the system is asymptotically stable, both locally and globally, at the consumption-free equilibrium $E_0$ when $R_0 \le 1$, indicating controlled consumption levels. Conversely, when $R_0 > 1$, a new equilibrium $E^*$ with ongoing consumption emerges, where the system remains asymptotically stable. This model provides valuable insights into the influence of addiction treatment centers on fast-food consumption dynamics and identifies key factors for effective addiction management.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] G. Sogari, "Fast food and youth eating behaviors," Public Health Review, vol. 15, pp. 22-33, 2017.

[2] Z. Wang, "Fast food consumption and obesity in urban populations," Journal of Urban Health, vol. 29, pp. 150-160, 2020.

[3] D. Aldila, "Ecological model analysis of college student eating behaviors," Health Psychology Quarterly, vol. 12, pp. 45-60, 2018.

[4] C. Oh, "Mathematical modeling of obesity spread and control strategies," Journal of Mathematical Biology, vol. 79, pp. 225-240, 2021.

[5] N. H. Shah et al., "A mathematical model to investigate the impact of obesity on infertility," Journal of Applied Mathematics and Bioinformatics, vol. 12, pp. 105-120, 2020.
Dynamics and numerical analysis of a Fractional
Order Host-Parasite Model with Diffusion

**Communication Info**

**Authors:**

Chaima MOUTALIBI¹
Ahmed AGHRICHE ¹
Youssef EL HADFI ¹

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

**Keywords:**

(1) Parasite-host model

(2) Diffusion

(3) Fractional-order

(4) Caputo derivative

(5) Basic reproduction number

(6) Stability

**Abstract**

This study investigates a fractional-order SI parasite-host model that includes diffusion effects. It explores essential properties of the solutions, including existence, uniqueness, positivity, and boundedness, while considering spatial interactions. Additionally, the local and global stability of the equilibrium points are examined, with a particular focus on the basic reproductive number $R_0$. Simulations are conducted to illustrate the impact of diffusion and confirm the theoretical results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Brauer F, Castillo-Chavez C, Feng Z (2019) Mathematical models in epidemiology (Vol. 32). New York: Springer.

[2] Ezanno P, Vergu E, Langlais M, Gilot-Fromont E (2012) Modelling the dynamics of host-parasite interactions: basic principles. *New Frontiers of Molecular Epidemiology of Infectious Diseases*, 79-101.

[3] Li MY (2018) An introduction to mathematical modeling of infectious diseases (Vol. 2). Cham, Switzerland: Springer.

[4] Nisar KS, Farman M, Abdel-Aty M, Ravichandran C (2024) A review of fractional-order models for plant epidemiology. *Prog Fraction Differ Appl*, 10(3), 489-521.

[5] Sandev T, Tomovski Z (2019) Fractional equations and models. Theory and applications. Cham, Switzerland: Springer Nature Switzerland AG.

[6] Zhang B, Cai Y, Wang B, Wang W (2019) Pattern formation in a reaction-diffusion parasite-host model. *Physica A: Statistical Mechanics and its Applications*, 525, 732-740.

[7] Zhou Y (2023) Basic theory of fractional differential equations. World scientific.
<figure><img src="image_54.png" /></figure>

# Comparative Analysis of Seismic Strengthening Systems for Existing Structures: Viscous Fluid Dampers vs. Traditional Bracing

## Communication Info.

**Authors:**

NOUR EDDINE
Abdelouahab 1,
RAMADANE
Abderazzak2,
MOUZZOUN
Miloud3,

1. International University of Casablanca, Laboratory « Mathematics and Engineering Sciences»,

2. International University of Casablanca, Laboratory « Mathematics and Engineering Sciences»,

3. Hassania School of Public Works Laboratory « of Civil Engineering, Hydraulics, Environment, and Climate (LaGCET) »,

**Keywords:**

Nonlinear dynamic analysis, Shear wall strengthening, Viscous fluid damper strengthening, Energy balance, Seismic performance, Vulnerability, Structural stiffness, Energy dissipation.

## Abstract

As part of the rehabilitation of existing reinforced concrete structures, which are often under-designed to withstand seismic loads, selecting an appropriate strengthening strategy is a crucial challenge. Traditional approaches mainly rely on increasing stiffness by adding reinforced concrete shear walls, an effective but restrictive solution due to its impact on architectural configuration, additional loads, work complexity, and sometimes the need for foundation resizing.

This study presents a detailed comparison between two strengthening methods: the use of linear and nonlinear viscous fluid dampers and the traditional column-wall system. The objective is to assess their respective effectiveness in reducing dynamic response and improving structural stability under seismic loading.

The analysis is conducted on a structure equipped with diagonal viscous fluid dampers at each floor, allowing energy dissipation through either a linear or nonlinear behavior. The results show that nonlinear dampers, characterized by a nonlinearity parameter $\alpha\alpha\alpha\alpha$ (0 < $\alpha\alpha\alpha\alpha$ < 1) appearing in the equation of the force generated by the damper:

$$F_d(t) = C_{NL}|\dot{x}|^{\alpha}\operatorname{sgn}(\dot{x}),$$

outperform linear dampers in terms of efficiency for the same damping coefficient and equivalent stiffness.

In comparison, the column-wall system provides reinforcement through stiffness $K$:

$$K_{voile} = \frac{12 EI}{h^3}$$

limiting lateral displacements but increasing internal forces within the structure.

The study also proposes a simplified procedure to adjust the damping coefficient of linear devices to match the performance of nonlinear dampers. The results highlight that while the column-wall bracing system is a robust solution in terms of stiffness, viscous dampers offer a more flexible and efficient alternative for energy dissipation, thereby reducing internal forces and minimizing heavy interventions on the existing structure.

These findings emphasize the importance of selecting the appropriate strengthening system based on structural and architectural constraints, adopting an optimized approach to ensure the stability and resilience of buildings against earthquakes.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References:**

[1]. M.C. Constantinou, P. Tsopelas, W. Hammel, A.N. Sigaher Toggle-brace-damper seismic energy dissipation system. J Struct Eng 127 (2) (2001) 105-12

[2]. Y.T. Chen, Y.H. Chai, Effects of brace stiffness on performance of structures with supplemental Maxwell model-based-damper systems. Earthquake Eng Struct Dyn 40 (2011) 75-92

[3]. T. Soong, B. Spencer, Supplement energy dissipation: State-of-the-art and state-of-the-practice. Eng Struct 24 (3) (2002) 243-259.

[4]. I. Takewaki (2009) Building control with passive dampers: Optimal performance-based design for earthquakes. Wiley, Singapore
Three-Parameter Estimation of the Stochastic Generalized
Rayleigh Diffusion Process

**Communication Info**

**Authors:**

Yassine CHAKROUNE¹
Ahmed NAFIDI¹

¹ Laboratory of Systems
Modelization and Analysis for
Decision Support (LAMSAD),
Hassan First University of
Settat, National School of
Applied Sciences of Berrechid,
Morocco

**Keywords:**

(1) Generalized Raleigh
distribution;

(2) Stochastic diffusion
process;

(3) Maximum likelihood
estimation;

(4) Simulated annealing;

(5) Statistical inference;

**Abstract**

Modeling real data using stochastic processes is a very
useful and powerful tools for many fields of research,
such as science and technology, infectious diseases,
biology and others. In this context, we introduce a new
stochastic diffusion process related the generalized
Rayleigh distribution (see, [3]). Then, we identify the
analytic solution of the stochastic differential equation,
the transition probability density function and the mean
functions (see,[2,6]). To estimate the three process
parameters in this process, we use the maximum
likelihood method based on discrete sampling (see, [1,
4]). The system of likelihood equations has no explicit
solution, so the form of the maximum likelihood
estimators cannot be obtained. It is essential to use
numerical methods such as the simulated annealing
algorithm (see, [5, 7]). We will finish by investigating
the possibility of using this new process to fit and
predict simulated data.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Y. Ait-Sahalia, **Maximum-likelihood estimation of discretely sampled diffusion: a closed form approximation approach** ; Econometrica 70, 223-262 (2002).

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

[3] H.D. Biçer, *Properties and inference for a new class of generalized Rayleigh distributions with an application*; Open Mathematics 17(1), 700-715 (2019).

[4] Nafidi, A.; Chakroune, Y.; Gutiérrez-Sánchez, R.; Tridane, A. Forecasting the Active Cases of COVID-19 via a New Stochastic Rayleigh Diffusion Process. *Fractal Fract.* **2023**, *7*, 660.
https://doi.org/10.3390/fractalfract7090660

[5] S. Kirkpatrick, C.D. Gelatt and M.P. Vecchi, *Optimization by simulated annealing*; *Science* **220**(4598), 671-680 (1983).

[6] Azri Abdenbi, E., Ahmed, Nafidi., & Yassine, Chakroune. Stochastic generalized Rayleigh diffusion process: computational strategies and statistical analysis. International Journal of Computer Mathematics, (2024). 1-16.
https://doi.org/10.1080/00207160.2024.2439324

[7] P. Roman-Roman, D. Romero, M.A. Rubio and F. Torres-Ruiz, *Estimating the parameters of a Gompertz-type diffusion process by means of simulated annealing* ; Applied Mathematics and Computation 218, 5121-5131 (2012).
<figure><img src="image_55.png" /></figure>

Viability results for first-order functional differential
inclusions with $\phi$-Laplacian in Banach spaces

**Communication Info**

**Authors:**

Najib ASKOURAYE¹

Myelkebir AITALIOUBRAHIM²

¹ Polydisciplinary Faculty of
Khouribga, Khouribga, Maroc

² Polydisciplinary Faculty of
Khouribga, Khouribga, Maroc

**Keywords:**

(1) Viability

(2) measurability

(3) Multifunction

(4) selection

(5) functional differential
inclusion

**Abstract**

In this work, we prove the existence of solutions the existence of solutions for the specified functional differential inclusion

$$ \begin{cases} (\phi(x(t)))' \in F(t, T(t)x), \text{ a.e. on } [0, \tau]; \\ x(s) = \varphi(s), \forall s \in [-a, 0]; \\ x(t) \in C(t), \forall t \in [0, \tau]. \end{cases} $$

The existence of the solution is obtained under the following conditions :

(H1) $C: [0,1] \to 2^E$ is a set-valued map with closed graph and $\mathcal{K}: [0,1] \to C_a$ is a set-valued map defined by $\mathcal{K}(t) = \{\varphi \in C_a, \varphi(0) \in C(t)\}$ and $F: \text{Gr}(\mathcal{K}) \to 2^E$ is a set-valued map with nonempty closed values, measurable with respect to the first argument and Lipschitz continuous with respect to the second argument and integrably bounded.

(H2) $\phi: E \to E$ is a homeomorphism function.

(H3) (Tangential condition) For each measurable function $v(\cdot): [0,1] \to E$, for all $\rho > 0$, $t \in [0,1]$ and $\psi \in \mathcal{K}(t)$, there exists $f \in S_{v,\rho}(\psi)$ such that

$$ \liminf_{h \to 0^+} \frac{1}{h} d \left( \psi(0) + \int_t^{t+h} f(s) ds, \phi(C(t+h)) \right) = 0. $$

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Aitalioubrahim, Viability result for semilinear functional differential inclusions in Banach spaces, Carpathian Mathematical Publications, 13, 2, 2021, 395-404.

[2] M. Aitalioubrahim, Viability result for higher-order functional differential inclusions, Methods of Functional Analysis and Topology, 26, 3, 2020, 189-200.

[3] M. Aitalioubrahim, On viability result for first order functional differential inclusions, Mat. Vesnik, 70, 4, 2018, 283-291.

[4] M. Aitalioubrahim, A viability result for functional differential inclusions in Banach spaces, Miskolc Math. Notes, 13, 1, 2012, 3-22.

[5] H. Brézis and F.E. Browder, A general principle on ordered sets in nonlinear functional analysis, Advances Math, 21, 3, 1976, 355-364.
Study of $ \psi $-Hilfer Fractional Fuzzy Hybrid Integro-Differential Equations

**Communication Info**

**Authors:**

Samira ZERBIB¹

Khalid HILAL¹

Ahmed KAJOUNI¹

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

**Keywords:**

(1) Fuzzy hybrid equation

(2) Fuzzy $ \psi $-Hilfer derivative

(3) Fixed point theorem

**Abstract**

Perturbation techniques are essential in the analysis of nonlinear dynamical systems that are difficult to solve or study directly. The inherent nonlinearity of such systems often lacks the smoothness required for investigating the existence and other properties of solutions. However, introducing perturbations allows these problems to be approached using existing analytical methods from different perspectives. Dynamical systems modified in this way are referred to as hybrid differential equations.

This manuscript focuses on establishing the existence of solutions for a class of fuzzy nonlinear $\psi$-Hilfer fractional differential equations. Our approach relies on the extended $\psi$-Hilfer fractional derivative of order $q, \sigma \in (0,1)$, applied to fuzzy functions, combined with the Dhage fixed point theorem. To illustrate the applicability of our findings, we conclude with an example demonstrating how the results can be utilized.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Samira Zerbib, Khalid Hilal, and Ahmed Kajouni. Some new existence results on the hybrid fractional differential equation with variable order derivative. Results in Nonlinear Analysis 6.1 (2023): 34-48.

[2]. D. Qiu, W. Hhang, C. Lu. On fuzzy differential equations in the quotient space of fuzzy numbers, Fuzzy set. Syst., 295 (2016), 72-98.

[3] Khalid Hilal, Ahmed Kajouni, and Samira Zerbib. Hybrid fractional differential equation with nonlocal and impulsive conditions. Filomat 37.10 (2023): 3291-3303.

[4] B.C. Dhage, V. Lakshmikantham, Basic results on hybrid differential equations, Nonlinear Anal. Hybrid 4 (2010) 414-424.

[5] B.C. Dhage, On a fixed point theorem in Banach algebras with applications, Appl. Math. Lett. 18 (2005) 273-280.
<figure><img src="image_56.png" /></figure>

$N_{\alpha}^{F}$ Fractional Semi-Groups Of Operators

**Communication Info**

**Authors:**

Rachid Bahoul<fnref n="1" />

Houssame Rachad <fnref n="2" />

Thabet Abdeljawad<fnref n="3" />

**Keywords:**

$N_{\alpha}^{F}$ Fractional Semi-Groups.

Fractional differential
equation.

Mean value Theorem.

Mild solution

**Abstract**

Our aim in this work is to introduce a new definition of the J. E. Napoles and M. N. Quevedo derivative in [1] and to generalize some fundamental calculus theorems, such as the Mean Value Theorem and Rolle's Theorem. Additionally, we extend the classical properties of semigroups for this derivative, including strong continuity and differentiability, along with its generator and its properties. These results allow us to define mild solutions for the fractional Cauchy problem. We also provide an example using the well-known translation semigroup. This theory can be applied in the future to solve problems in a wide range of domains, such as population dynamics.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] J. E. Napoles, M. N. Quevedo, On the Oscillatory Nature of Some Generalized Emden-Fowler Equation Punjab University Journal of Mathematics Vol. 52(6)(2020) pp. 97-106.

<footnote n="1">¹ Department of Mathematics,
polidisciplinary faculty, Sultan
Moulay Slimane University, Beni
Mellal, Morocco.</footnote>

<footnote n="2">² Department of Mathematics,
polidisciplinary faculty, Sultan
Moulay Slimane University,
Beni Mellal, Morocco.</footnote>

<footnote n="3">³ Department of Mathematics
and Sciences, Prince Sultan
University, Riyadh 11586, Saudi
Arabia.</footnote>
Existence of weak solutions for a (p(x), q(x))-
elliptic system via topological degree

**Communication Info**

**Authors:**

Abdellatif YASSIR¹

Mostafa EL MOUMNI ²

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

**Keywords:**

(1) p(x)-Laplacian

(2) weak solution

(3) topological degree

(4) variable exponent Sobolev space

(5) variable exponent Sobolev space

**Abstract**

This work examines the existence of weak solutions for (p(x),q(x))-elliptic systems. The proof is based on Berkovits' topological degree theory, under precise conditions imposed on the nonlinear terms.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] M. Ait Hammou and E. H. Rami, Existence of weak solutions for a p(x)-Laplacian equation via topological degree, Izvestiya IMI UdGU, 59, 15-24 (2022).

[2] J. Berkovits, Extension of the Leray-Schauder degree for abstract Hammerstein type mappings, Journal of Differential Equations, 234(1), 289-310, 2007.

[3] M. Ait Hammou, E. Azroul and B. Lahmi, Existence of solutions for p(x)-Laplacian Dirichlet problem by topological degree, Bulletin of the Transilvania University of Bras, ov. Ser. III: Mathematics, Informatics, Physics, 11 (60) (2018), no. 2, 29-38.
A Functional Principal Component Analysis
Approach to Conditional Copula Estimation

**Communication Info**

**Authors:**

Cheikh Tidiane SECK¹

Toihir Soulaimana DJALOUD ²

¹ Université Alioune Diop,
Bambey, Sénégal

² Université Alioune Diop,
Bambey, Sénégal

**Keywords:**

(1) Conditional copula;

(2) Karhunen--Lo\'eve
expansion;

(3) Nonparametric
estimation.

**Abstract**

Conditional copula model arises when the dependence
between random variables of interest is influenced by
another covariate. Despite its relevance for many
applications in dependence modelling, there are few
nonparametric approaches devoted to its estimation.

In this paper, we propose a new nonparametric
approach which is based on functional principal
component analysis. We consider the conditional copula
process $C_X(u, v): 0 \le u, v \le 1$, where $X$ designs the
covariate, and give its Karhunen--Loève expansion, from
which we derive our estimator. We then establish its
$\sqrt{n}$-consistency and weak convergence in $L^2([0,1]^2)$ to a
Gaussian limit process with explicit covariance function.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Irène Gijbels, Marek Omelka, and Noël Veraverbeke. Estimation of a copula when a covariate affects only marginal distributions. Scand. J. Statist., 42, 2015a,1109-1126.

[2] Irène Gijbels, Marek Omelka, and Noël Veraverbeke. Partial and average copulas and association measures. Electronic Journal of Statistics, 9, 2015b, 2420-2474.

[3] Piotr Kokoszka and Matthew Reimherr. Introduction to functional data analysis. Chapman Hall/CRC, 2017.

[4] Noël Veraverbeke, Marek Omelka, and Irene Gijbels. Estimation of a conditional copula and association measures. Scandinavian Journal of Statistics, 38(4), 2011, 766-780.

[5] Andrew J Patton. Modelling asymmetric exchange rate dependence. International economic review, 47(2), 2006,27-556.
Optimal Control Problem for a Semilinear Wave
Equation

**Communication Info**

Abdelhak Bouhamed¹
Abella El Kabouss²
Hassane Bouzahir¹

¹LISTI Laboratry, National
School of Applied Sciences,
Agadir, Morocco,

²Faculty of Economics and
Management-Guelmim, Ibn
Zohr University, Morocco.

**Keywords:**

(1) Wave equation

(2) Boundary bilinear
control

(3) Optimal control
problem.

**Abstract**

The aim of this work is to study the optimal control of a semilinear wave equation, where the control enters the system bilinearly through the boundary. The objective is to determine a distributed control that drives the system from an initial state to a desired one in finite time while minimizing a quadratic cost functional. Our goal is to prove the existence of an optimal control within a closed convex set. Then, by exploiting the differentiability of the cost functional with respect to the control, we establish the necessary conditions that an optimal control must satisfy.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Pazy. Semigroups of linear operators an applications to PDE.Springer-Verlag, New York, 1983.

[2] E. Zerrik and A.El Kabouss. Bilinear boundary control problem of an output of parabolic systems, pages 193-203. 012020.

[3] Bouhamed, A., Elkabouss, A., & Bouzahir, H. (2022). Bilinear boundary optimal control of a Kirchhoff plate equation. Results in Control and Optimization, 9, 100179.

[4] Bouhamed, A., El Kabouss, A., & Bouzahir, H. (2022). Bilinear Boundary Optimal Control of a Nonlinear Kirchhoff Plate Equation. In International Conference on Research in Applied Mathematics and Computer Science (Vol. 2022). ICRAMCS 2022.

[5] Bouhamed, A., Elkabouss, A., de Carvalho, P. P., & Bouzahir, H. (2024). Boundary optimal control problem of semi-linear Kirchhoff plate equation. Nonlinear Analysis: Real World Applications, 80, 104146.

[6] M.Liang. Bilinear optimal control for a wave equation. Mathematical Models and Methods in Applied Sciences, 9(01):45-68, 1999.
<figure><img src="image_57.png" /></figure>

# A New Estimation Approach for Structural Equation Models

## Communication Info

**Authors:**

Zouhair El Hadri¹

Sabah Laarif²

¹ Faculty of Sciences, Mohammed V
University, Rabat, Morocco

² Faculty of Sciences, Mohammed V
University, Rabat, Morocco

**Keywords:**

(1) Structural Equation Modeling

(2) Implied covariance matrix

(3) Finite iterative method

## Abstract

Structural Equation Modeling is a multivariate technique that analyzes causal relationships between latent variables and their measured indicators, forming a hypothesis on their specific pattern of relations. The estimation process is a key step in modeling, often performed with the popular BFGS algorithm ([1],[2]). A new approach was recently introduced by El Hadri et al. in the context of Path Analysis models ([3], [4]). This method has strong convergence properties that outperform the BFGS algorithm, offering a simple and effective alternative. In this paper, we extend this new procedure to Structural Equation Models while maintaining its strong convergence properties and superior efficiency compared to the classical method.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Bollen, K. A. (1989). *Structural equations with latent variables*. John Wiley & Sons.

[2] Bentler, P. M. (1989). EQS Structural Equations Program Manual. Los Angeles, CA, BMDP Statistical Software Pages.

[3] Z. El Hadri, A. Sahli, M. Hanafi, "Simple and fast convergent procedure to estimate recursive path analysis model," *Behaviormetrika*, 50, 2023, 317-333. https://doi.org/10.1007/s41237-022-00181-z

[4] Z. El Hadri, A. Sahli, S. Ebnou Abdem, M. Hanafi, "Extending El-Hadri-Sahli-Hanafi procedure for path analysis with non-standardized variables," *Qual Quant*, 2024. https://doi.org/10.1007/s11135-024-01932-8

[5] El Hadri, Z., & Hanafi, M. (2015). The Finite Iterative Method for calculating the correlation matrix implied by a recursive path model. *Electronic Journal of Applied Statistical Analysis*, 8(1), 84-99. https://doi.org/10.1285/i20705948v8n1p84
Approximate Optimality and Approximate
Duality for Multiobjective Fractional Interval-
valued Problems

**Communication Info**

**Authors:**

Moustaid Mohamed Bilal¹
Dali Issam ²

¹ Chouaib Doukkali Universit,
Faculty of sciences, El Jadida,
Morocco

**Keywords:**

(1) Fractional interval
multivalued programming
problem

(2) LU-Pareto solutions

(3) LU-convexity

**Abstract**

In this article, we establish approximate Karush-Kuhn-Tucker necessary and sufficient optimality conditions for approximate LU-Pareto solutions of a multiobjective fractional interval valued programming problem, where the numerator and denominator of the objective functions are assumed to be interval-valued functions. Furthermore, two duals, namely Wolfe and Mond-Weir duals, are introduced, and duality results are proven under LU-convexity assumptions. Several examples are provided to illustrate the results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Ahmad I, Singh D, Dar BA. Optimality conditions in multiobjective programming problems with interval valued objective functions. Control and Cybernetics. 2015;44(1).

[2] Antczak T, Abdulaleem N. Optimality conditions for E-differentiable vector optimization problems with the multiple interval-valued objective function. Journal of Industrial & Management Optimization. 2020 Nov 1;16(6).

[3] Tung LT. Karush-Kuhn-Tucker optimality conditions and duality for convex semi-infinite programming with multiple interval-valued objective functions. Journal of Applied Mathematics and Computing. 2020 Feb;62(1):67-91.

[4] Antczak T. On first and second order multiobjective programming with interval-valued objective functions. Applicable Analysis. 2024 Apr 12;103(6):1098-117.
# A New Approach to Modeling Multidrug-Resistant Tuberculosis

**Communication Info**

**Authors:**

Laouina aziza¹

Baheraoui Zuhair¹

El Rhoubari Zineb¹

¹ Faculty of sciences,
Chouaïb Doukkali
University, El jadida,
Morocco.

**Keywords:**

(1) Epidemic models,

(2) Tuberculosis

(3) Global stability.

**Abstract**

Our objective in this study is to introduce and analyze a new drug-resistant tuberculosis epidemic model [1]. We determine the basic reproduction number R0 [2] and conduct a sensitivity analysis [3]. Furthermore, we investigate the existence and stability of both the disease-free and endemic equilibrium states [4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Yu, Y., Shi, Y., and Yao, W. (2018). Dynamic model of tuberculosis considering multi-drug resistance and their applications. *Infectious Disease Modelling*, **3**, 362–372.

[2] P. van den Driessche and James Watmough. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission (2002).

[3] Chitnis, N., Hyman, J. M. and Cushing, J. M. (2008). Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. *Bulletin of Mathematical Biology*, **70**(5), 1272–1296.

[4] Liu, X. and Yang, L. (2012). Nonlinear Analysis: Real World Applications Stability analysis of an SEIQV epidemic model with saturated incidence rate. *Nonlinear Analysis: Real World Applications*, **13**(6), 2671–2679.
<figure><img src="image_58.png" /></figure>

# Existence, Uniqueness, and Stability of Solutions for Nonlinear Neutral Volterra-Fredholm Integro-Differential Equations with Caputo Fractional Derivatives

## Communication Info

**Authors:**

El Habib BANOUISSE¹
M'hamed ELOMARI¹
Aziz EL GHAZOUANI¹

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

**Keywords:**

(1) Caputo fractional derivatives

(2) Existence and uniqueness

(3) Krasnoselskii fixed point theorem

(4) Ulam-Hyers-Rassias stability

(5) Neutral Volterra-Fredholm integro-differential equations

## Abstract

This work investigates a non-linear Volterra-Fredholm integrodifferential equation with Caputo fractional derivatives and particular order constraints. The work rigorously proves the existence and uniqueness of analytical solutions using the Banach principle. It also provides a unique result on the presence of at least one solution, which is backed by strict criteria derived from the Krasnoselskii fixed point theorem. Furthermore, the study includes neutral Volterra-Fredholm integro-differential equations, broadening the application of the results. Furthermore, the research investigates the idea of generalized Ulam Hyers-Rassias stability for the given solutions, which provides important insights into their long-term behavior. To emphasize the practical relevance and trustworthiness of the conclusions, an illustrated examples is provided, successfully proving the theoretical discoveries' application.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science, 2006.

[2] B. C. Dhage, S. K. Ntouyas, Existence results for boundary value problems for fractional hybrid differential inclusions, Topol. Method Nonlinear. Anal., 44 (2014), 229-238.

[3] B. Ahmad, S. Sivasundaram, Some existence results for fractional integro-differential equations with nonlinear conditions, Commun. Appl. Anal., 12 (2008), 107-112.
Commutativity of 3-prime near-rings involving
homoderivations

**Communication Info**

**Authors:**

Slimane EL AMRANI¹
Abderrahmane RAJI¹

¹ LMACS Laboratory, Faculty
of Sciences and Technology,
Sultan Moulay Slimane
University, Beni Mellal,
Morocco

**Keywords:**

(1) Prime near-rings

(2) homoderivations

(3) Commutativity

**Abstract**

Throughout this paper, N will be a left near-ring. An additive mapping $d: N \to N$ is said to be a derivation if $d(xy) = d(x)y +xd(y)$ for all $x,y \in N$ or equivalently as noted in [4], that $d(xy) = xd(y) + d(x)y$ for any $x,y \in N$. In [2], the notion of homoderivation on ring was introduced by El Sofy as follows: An additive mapping $h: N \to N$, is called a homoderivation if $h(xy) = h(x)h(y)+xh(y) + h(x)y$ holds for all $x, y \in N$.

Many results on commutativity in prime and semi-
prime rings admitting suitably constrained derivations,
generalized derivations, and homoderivations have been
published in the literature (see [1], [3] and [4]).

The main objective of the present paper is to investigate
homoderivations in 3-prime near-rings that satisfy certain
differential identities

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Boua, L. Oukhtite and A. Raji, Jordan ideals and derivations in prime near-rings, Comment. Math. Univ. Carolin., 55(2) (2014), 131-139.

[2] M. M. El Sofy, Rings with some kinds of mappings, M. Sc. Thesis, Cairo University, Branch of Fayoum, (2000).

[3] A. Raji, M. Oukessou and A. Belharrate, Jordan ideals with multiplicative derivations in 3-prime near-rings, Advanced Mathematical Models and Applications., 7(2) (2022), 214-222.

[4] X. K. Wang, Derivations in prime near-rings, Proc. Amer. Math. Soc., 121(1994), 361-366.
<figure><img src="image_59.png" /></figure>

Le Marketing expérientiel et e-commerce : Le rôle des facteurs atmosphériques numériques dans le comportement d'achat des consommateurs

**Communication Info**

**Authors:**

Loubna EL HATTAB ¹

Tarik ZARI ²

¹ Doctorante, Faculté des Sciences Juridiques Economiques et Sociales Mohammed, Mohammed, Morocco

² Professeur, Faculté des sciences juridiques, économiques et sociales d'Ain Sebâa, Casablanca, Morocco

**Keywords:**

(1) Atmosphère des sites web

(2) E-commerce

(3) Intention d'achat

(4) Emotion

(5) SOR

**Abstract**

Avec l'essor d'Internet haut débit et des technologies immersives, l'impact des canaux de distribution sur l'expérience et le comportement des consommateurs suscite un intérêt croissant. Depuis l'article fondateur de Kotler (1973) sur les « atmospherics », les chercheurs en marketing et en psychologie ont étudié l'influence des éléments d'ambiance sur les réponses émotionnelles et comportementales des consommateurs [1]. D'abord explorés dans les magasins physiques [2], [3], ces facteurs ont ensuite été transposés aux environnements numériques avec le développement du commerce en ligne [4].

Aujourd'hui, alors que l'expérience d'achat devient de plus en plus immersive et interactive, l'impact des atmosphères numériques – comprenant l'ambiance du site web, son design et la présence sociale – sur la prise de décision des consommateurs suscite un intérêt croissant [5], [6]. Pourtant, la recherche sur ce sujet demeure fragmentée.

Dans ce travail, nous nous intéressons à étudier l'influence de l'atmosphère numérique sur le comportement d'achat des consommateurs, en s'appuyant sur une revue de la littérature antérieure. Plus précisément, cette étude poursuit deux objectifs : (1) identifier les cadres théoriques majeurs expliquant l'impact des atmosphères numériques sur les émotions et l'intention d'achat des consommateurs ; (2) mettre en évidence les lacunes existantes et proposer des pistes de recherche futures pour enrichir ce champ en pleine évolution. Une étude empirique sera présentée pour validation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Kotler, Philip. "Atmospherics as a marketing tool." Journal of retailing 49.4 (1973): 48-64.

[2] Bitner, Mary Jo. "Servicescapes: The impact of physical surroundings on customers and employees." Journal of marketing 56.2 (1992): 57-71

[3] Turley, Lou W., and Ronald E. Milliman. "Atmospheric effects on shopping behavior: a review of the experimental evidence." Journal of business research 49.2 (2000): 193-211

[4] Eroglu, Sevgin A., Karen A. Machleit, and Lenita M. Davis. "Atmospheric qualities of online retailing: A conceptual model and implications." Journal of Business research 54.2 (2001): 177-184.

[5] Basu, Rituparna, Justin Paul, and Kandarp Singh. "Visual merchandising and store atmospherics: An integrated review and future research directions." Journal of Business Research 151 (2022): 397-408.

[6] Hsieh, Jung-Kuei, et al. "Customer response to web site atmospherics: Task-relevant cues, situational involvement and PAD." Journal of Interactive Marketing 28.3 (2014): 225-236.
<figure><img src="image_60.png" /></figure>

The Navier-Stokes Equations: Mathematics' Greatest Unsolved Challenge

**Communication Info**

**Authors:**

MOHAMMED EL ALAOUI<fnref n="1" />

MOULAY RCHID SIDI AMMI<fnref n="2" />

**Keywords:**

(1) Navier-Stokes equations

(2) nonlinear partial differential equation

**Abstract**

Navier Stokes, the cornerstone of fluid dynamics, envelops the complex interaction of non-linear partial differential equations that govern phenomena from turbulent flows to atmospheric movement. This enduring sporting challenge, particularly explores the problem of Fefferman's Millennium Award [1], which seeks to demonstrate the existence and smoothness of solutions in three dimensions or evidence of a time-limited explosion. Based on foundational insights from Landau and Lifshitz [2], we emphasize the equations "pivotal role in modeling physical systems, while Pope [3] illuminates the complexities of turbulence - vortex expansion and energy dissipation - that challenge analytical accuracy in 3D. In contrast, Kuksin and Shirikyan [4] make progress in 2D disturbance via random methods, highlighting the disparity with unresolved 3D status. Despite extensive practical applications, theoretical foundations remain elusive, with non-internal and non-local influences forming enormous barriers. Solving this puzzle promises transformative leaps in mathematics and applied science, enhancing Navier Stokes' equations as specific limits for human investigation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Fefferman, C. L., "Existence and Smoothness of the Navier-Stokes Equation," *Clay Mathematics Institute Proceedings*, 1, 2000, 1-12.

[2] Landau, L. D., Lifshitz, E. M., "Fluid Mechanics," *Course of Theoretical Physics*, 6, 1987, 1-536.

[3] Pope, S. B., "Turbulent Flows," *Cambridge University Press*, 1, 2000, 1-771.

[4] Kuksin, S., Shirikyan, A., "Mathematics of Two-Dimensional Turbulence," *Cambridge Tracts in Mathematics*, 194, 2012, 1-314.

<footnote n="1">¹ FST, ERRACHIDIA, MOROCCO</footnote>

<footnote n="2">² FST, ERRACHIDIA, MOROCCO</footnote>
<figure><img src="image_61.png" /></figure>

Epidemic Model of Tuberculosis: Analysis of
Dynamic Transmission and Simulation

**Communication Info**

**Authors:**

Soufiane HAMANI¹

¹ FSDM, USMBA, FEZ,
MOROCCO

**Keywords:**

(1) Tuberculosis

(2) SIRI

(3) Modeling

**Abstract**

In this work we study a mathematical modeling of tuberculosis transmission. The study will use a SIRI (Susceptible-Infected-Recovered-Immune) model to analyze the dynamics of disease transmission.

We solve the model numerically and we present the simulation results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] N. Bame, S. Bowong, J. Mbang, G. Sallet, J. Tewa. Global stability analysis for SEIS models with nlatent classes, Math. Biosci. Eng. 5 (1) (2008) 20-33.

[2] E. Beretta, V. Capasso. On the general structure of epidemic systems. Global asymptotic stability, Comput. Math. Appl., Part A, 12 (1986) 677-694.

[3] P. van den Driessche, L. Wang, X. Zou, Modeling diseases with latency and relapse, Math. Biosci. Eng. 4 (2007) 205-219.
# Exponential stabilization of wave equation with control saturation

## Communication Info

**Authors:**

Wafae Abaakil
Mohamed Laabissi²

¹ Chouaib Doukkali University,
El jadida, Morocco

² Chouaib Doukkali University,
El jadida, Morocco

**Keywords:**

(1) Exponential stability

(2) nonlinear semigroup

(3) wave equation

## Abstract

This work investigates the exponential stabilization of a wave equation subject to saturation. The system is governed by a partial differential equation(PDE) with a nonlinear saturation function applied to the control input, ensuring bounded actuation[1]. In contrast with the existing works [2], the control *f* is given by $f(s,t) = -\mathrm{sat}(a(s)x(t,s))$ with *sat* is the saturation function [3] and *a(s)* is a positive function that satisfies some specific conditions [4]. The well posedness of the system is proved by using the theory of nonlinear semigroups [5], and the exponential stability is shown by an appropriate Lyapunov functional. Numerical simulations are provided to validate the theoretical results, demonstrating the effectiveness of the proposed approach in stabilizing the wave equation while respecting input constraints.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Binid, A., Taboye, A.M., Laabissi, M, Cone-bounded feedback laws for linear second order system, Evolution Equations & Control Theory, vol.12(4), 2023, pp. 1174-1192

[2] Enrike, Z.: Exponential decay for the semilinear wave equation with locally distributed damping. Communications in Partial Differential Equations, vol. 15(2), 1990, pp. 205-235.

[3] Marx, S., Chitour, Y., Prieur, C., Stability results for infinite-dimensional linear control systems subject to saturations, European Control Conference (ECC), 2018, pp. 2995-3000.

[4] Taboye, A.M., Laabissi, M., Exponential stabilization of a linear korteweg-de vries equation with input saturation, Evolution Equations and Control Theory, vol. 11(5), 2022, pp: 1519-1532.

[5] Miyadera I, Nonlinear semigroups. Translations of mathematical monograph, vol. 109, 1992.
Modeling Inflation in the Euro Area: Approach and Perspectives

**Communication Info**

**Authors:**

Kaoutar EL MOUSSAOUY¹

Mohammed MESTARI¹

Mohammed BENHOUAD ¹

¹ ENSET, Mohammadia,
Morocco

**Keywords:**

(1) inflation

(2) Modeling

(3) euro area

(4) Economic Dynamics

(5) Monetary Policy

**Abstract**

This paper aims to model inflation in the euro area to analyze its dynamics and identify the key factors that drive it. The study will first review some existing models, notably Taylor's famous model [1] and the Vector Autoregression (VAR) econometric model [2], to provide a theoretical foundation. Using a quantitative approach, it will then develop a model to enhance the understanding of inflation trends and their interactions with the economy. The objective is to assess recent developments and provide insights into the underlying mechanisms while considering economic uncertainties and the policies implemented to stabilize inflation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Taylor, J. B., Discretion versus policy rules in practice, Carnegie-Rochester Conference Series on Public Policy, 39, 1993, 195-214.

[2] Óscar Arce, Matteo Ciccarelli, Antoine Kornprobst, Carlos Montes-Galdón, What caused the euro area post-pandemic inflation?, 2023, 7-14.
<figure><img src="image_62.png" /></figure>

Locally meshfree RBF kernel-based method for solving
multidimensional hyperbolic equations

**Communication Info**

**Authors:**

Lanceni KEITA¹
Lahcen AZRAR¹
Ateq Ahmed AL-GHAMEDI²

¹Research Center STIS, M2CS,
Department of Applied
Mathematics and Informatics,
ENSAM, Mohammed V
University, Rabat, Morocco

²Faculty of Sciences,
Department of statistics, King
Abdulaziz University,Jeddah,
Saudi Arabia

**Keywords:**

(1) Meshfree method

(2) Hyperbolic equations

(3) Stability and simulation

**Abstract**

A methodological approach based on the Wendland compactly supported radial basis function (RBF) [1] is elaborated and applied to various nonlinear multidimensional hyperbolic equations on irregular domains. The focus is firstly on the Burgers type equationdefined by the following equation [2]:(*)

$$ 
\begin{cases} 
\frac{\partial u}{\partial t}(x,t) + \mu(u(x,t) \cdot \nabla) u(x,t) - \zeta Lu(x,t) \\ 
= f(x,t), \quad \text{for } x \in \Omega \text{ and } t \in [t_0; T] 
\end{cases} 
$$

where L is a linear partial differential operator, f and g are known functions and u is the velocity component. A Method of Lines (MOL) meshfree method is elaborated allowing to transform the partial differential problem (*) into a nonlinear ordinary differential system, solved with an explicit scheme ensuring efficient updates.

Key challenges addressed are the implementation of various mixed boundary conditionsand thehandling of irregular domains in meshfree methods. The scheme's stability is rigorously analyzed, and various computational tests are elaborated leading to a valuable tool for simulating complex engineering systems.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] L. Keita, L. Azrar and A.A. Al-Ghamedi. A local meshfree approach based on compactly supported radial basis functions for 2D coupled fluid dynamics PDEs on regular and irregular domains. Accepted in Engineering Analysis with Boundary Elements, 2025.

[2] A. Bouhamidi, M. Hached, K. Jbilou, A meshless RBF method for computing a numerical solution of unsteady Burgers'-type equations Computers and Mathematics with Applications, 68, 2014, 238-256.
Super-Recurrence of Elementary Operators

**Communication Info**

**Authors:**

LAKRIMI Hamza¹

AMOUCH Mohamed ²

¹,² *Laboratory of Fundamental Mathematics and their Applications LMFA, Department of Mathematics, Faculty of sciences, Chouaïb Doukkali University, 24000 El Jadida, Morocco.*

**Keywords:**

(1) Orbit

(2) Supercyclicity

(3) Recurrent operators

(4) Super-recurrent operators

(5) Elementary operators

**Abstract**

Let $X$ be a separable Banach space over the field $C$ of complex numbers, $B(X)$ the algebra of all bounded linear operators on $X$ and $(J, ||\cdot||_J)$ be an admissible Banach ideal of $B(X)$. For $A, B \in B(X)$, let

$L_A \in B(B(X))$, and $R_B \in B(B(X))$ be the left and the right multiplication operators, respectively. The two-sided multiplication $M_{A,B} \in B(B(X))$ is defined by $M_{A,B}(S)=(L_A R_B)(S)=ASB$ and the generalized derivation $\partial_{A,B} \in B(B(X))$ is defined by $\partial_{A,B}(S)=(L_A - R_B)(S)=AS-SB$.

The aim objective of this presentation is concerned to study the transmission of some proprieties related to super-recurrence from operators $A, B \in B(X)$ to their elementary operators $L_A, R_B, M_{A,B}$ and $\partial_{A,B}$ defined on an admissible Banach ideal of operators $(J, ||\cdot||_J)$.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Amouch, M., Benchiheb, O., On a class of super-recurrent operators. *Filomat*, **36**(11), 2022,3701-3708.

[2] Amouch, M. Lakrimi, H., Supercyclicity of Multiplication on Banach Ideal of Operators. Boletim da Sociedade Paranaense de Matemática, 40, 2022, 1-11.

[3] Amouch, M. Lakrimi, H., Recurrence and mixing recurrence of multiplication operators, Mathematica Bohemica, 149 (1), 2024.

[4] Bayart, F. Matheron, E., Dynamics of Linear Operators (Cambridge Tracts in Mathematics, 179). Cambridge University Press, Cambridge, 2009.

[5] Bonet, J., Martinez-Gimenez, F., Peris, A., Universal and chaotic multipliers on spaces of operators. J. Math. Anal. Appl. 297(2), 2004, 599-611.
# Solving the Flow Shop Scheduling Problem
by Two Metaheuristics

## Communication Info

**Authors:**

Hajar Sadki¹

¹ University, Hassan II of
Casablanca, FST Mohammed,
Morocco

**Keywords:**

(1) flow shop scheduling

(2) Metaheuristics

(3) Genetic algorithm

## Abstract

In this work, our subject is to solve a flow shop scheduling problem. The goal is to minimize the makespan of all jobs. We will use two efficient metaheuristics: the first is the iterative local search algorithm (ILS) and the genetic algorithm (GA) [1,2]. We will choose different sizes of the instance, and we will compare the result given by the metaheuristics. The numerical test shows that the genetic algorithm gives the best performance compared to the iterative local search algorithm.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Sadki, H., Aqil, S., Belabid, J., & Allali, K. (2024). Multi-Objective Optimization Flow Shop Scheduling Problem Solving the Makespan and Total Flow Time with Sequence Independent Setup Time. *Journal of Advanced Manufacturing Systems, 23*(01), 163-184.

[2] Sadki, H., Belabid, J., Aqil, S., & Allali, K. (2021, November). On permutation flow shop scheduling problem with sequence-independent setup time and total flow time. In *International Conference on Advanced Technologies for Humanity* (pp. 507-518). Cham: Springer International Publishing.
Existence and Uniqueness Results for Higher-Order Nonlinear
Fractional Differential Equations via Coincidence Degree Theory

**Communication Info**

**Authors:**

Sami BAROUDI¹
Abderrazak KASSIDI¹
Ali EL MFADEL¹
M'hamed ELOMARI¹

¹ Laboratory of Applied
Mathematics and Scientific
Computing, Sultan Moulay
Slimane University, Beni Mellal,
23000, Morocco.

**Keywords:**

(1) ψ-Caputo fractional derivative

(2) Mawhin's coincidence degree theory

(3) Fractional differential equations

(4) Banach contraction principle

(5) Adomian decomposition method

**Abstract**

In this paper, we introduce a new class of fractional differential equations involving the ψ-Caputo derivative of order α∈(2,3), addressing both theoretical foundations and numerical implementations. We establish the existence of solutions using Mawhin's coincidence degree theory and prove uniqueness via Banach's contraction principle. To tackle the computational challenges, we apply the Adomian decomposition method, ensuring high accuracy and efficiency. A detailed case study is provided to validate our approach, highlighting its practical relevance and potential applications in complex dynamic systems.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Baroudi, M. Elomari, A. El Mfadel, and A. Kassidi, Numerical solutions of the integro-partial fractional diffusion heat equation involving tempered ψ-caputo fractional derivative, Journal of Mathematical Sciences 271 (2023), 4, 555-567.

[2] A. El Mfadel, A. Kassidi, and H. Moujani, On parabolic problems with fractional q (z)-Laplacian operators and young measures. Journal of Elliptic and Parabolic Equations (2024), 1-17.

[3] A. Kassidi, S. Melliani, A. Sabiry, and G. Zineddaine, A weak solution to a Kirchhoff type problem with discontinuous nonlinearities. Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science (2023) 101-120.

[4] Z. Odibat. Numerical discretization of initial-boundary value problems for pdes with integer and fractional order time derivatives. Communications in Nonlinear Science and Numerical Simulation, 140 (2025), 108331.
Quasi-orthogonal extension property of
symmetric matrices

**Communication Info**

**Authors:**

Abderrahim Boussaïri¹

Brahim Chergui¹

Sarir Zaineb ¹

Mohamed Zouagui ²

¹ FSAC, University of Hassan II
Casablanca

² ISchool of Engineering,
International University of
Casablanca

**Keywords:**

(1) Symmetric matrix

(2) Principal sub-matrix

(3) Quasi-orthogonal matrix

(4) Quasi-orthogonal extension

(5) Quasi-orthogonal index

**Abstract**

An $n \times n$ real matrix $Q$ is quasi-orthogonal if $Q^T Q = qI_n$, for some positive real number $q$. If $M$ is a principal sub-matrix of a quasi-orthogonal matrix $Q$, then we say that $Q$ is a quasi-orthogonal extension of $M$. A class $\mathcal{M}$ of square matrices has the *quasi-orthogonal extension property* (QOEP for short) if every matrix $M$ in $\mathcal{M}$ has a quasi-orthogonal extension $Q$ in $\mathcal{M}$. For a class $\mathcal{M}$ that has QOEP, the *quasi-orthogonality index* of an $n \times n$ matrix $M \in \mathcal{M}$ is the least integer $d$, denoted by $\text{ind}(M)$, such that $M$ has a quasi-orthogonal extension in $\mathcal{M}$ of order $n + d$.

In this work, we focus on the class of symmetric matrices and prove that it has QOEP. Furthermore, we determine the quasi-orthogonality index for symmetric matrices.

**References**

[1] V. Belevitch. *Conference networks and Hadamard matrices*. Annales de la Societe scientifique de Bruxelles, 82(1):13-32, 1968.

[2] A. Boussaïri, B. Chergui, Z. Sarir, and M. Zouagui. *Quasi-orthogonal extension of skew-symmetric matrices*. arXiv preprint arXiv:2410.19594, 2024.

[3] A. Boussaïri, B. Chergui, Z. Sarir, and M. Zouagui. *Quasi-orthogonal extension of symmetric matrices*. arXiv preprint arXiv:2412.10197, 2024.

[4] G. Greaves and S. Suda. *Symmetric and skew-symmetric {0, ± 1}-matrices with large determinants*. Journal of Combinatorial Designs, 25(11):507-522, 2017.

[5] C. Koukouvinos and J. Seberry. *New weighing matrices and orthogonal designs constructed using two sequences with zero autocorrelation function-a review*. Journal of statistical planning and inference, 81(1):153-182, 1999.
<figure><img src="image_63.png" /></figure>

Compact operators on right quaternionic Banach spaces

**Communication Info**

**Authors:**

Somayya MOULAHARABBI<fnref n="1" />

Mohamed BARRAA<fnref n="2" />

**Keywords:**

(1) Quaternionic Banach space

(2) Compact operators

(3) Orthogonality

(4) Duality

**Abstract**

In recent years, the study of operators on quaternionic Banach spaces has gained significant attention due to its importance in both theoretical and applied mathematics. Among these, compact operators play a fundamental role in functional analysis, and their study in right quaternionic Banach spaces presents new challenges and insights. In this paper, we study compact operators on right quaternionic Banach spaces and extend Fredholm's alternative theorem to this setting. We first establish fundamental properties of compact operators in quaternionic Banach spaces. Then, we present and prove Fredholm's alternative theorem for quaternionic compact operators and explore its implications. Finally, we examine specific properties of the S-spectrum of these operators.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] H. Brezis, Analyse fonctionnelle, théorie et applications, Paris, New York, Masson (1983).

[2] F. Colombo and J.Gantner, Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes, Operator Theory: Advances and Applications, 274. Birkhauser, Cham, 2019.

[3] P. Cerejeiras, F. Colombo, U. Kahler and I. Sabadini, Perturbation of normal quaternionic operators, Trans. Amer. Math. Soc. 372(5), 3257-3281 (2019).

[4] M. Fashandi, Compact operators on quaternionic Hilbert spaces, Facta universitatis, series Mathematics and Informatics 28 (3) (2013).

[5] J. Gantner, Slice hyperholomorphic functions and the quaternionic functional calculus, Masters Thesis, 2014, Vienna University of Technology.

[6] R. Ghiloni, V. Moretti and A. Perotti, Continuous slice functional calculus in quaternionic Hilbert spaces, Rev. Math. Phys. 25(4) (2013), 1350006.

[7] C.S. Kubrusly, Spectral Theory of Operators on Hilbert Spaces, Birkhauser, Springer, New York, 2012.

[8] B. Muraleetharan and K. Thirulogasanthar, Fredholm operators and essential S-spectrum in the quaternionic setting, J. Math. Phys. 59, 103506 (2018).

[9] S. Moulaharabbi and M. Barraa, S-Spectrum of Quaternionic Right Linear Bounded Operators, Adv. Appl. Clifford Algebras 33, 25 (2023). https://doi.org/10.1007/s00006-023-01271-1.

[10] S. Moulaharabbi, M. Barraa and E. H. Benabdi, Numerical range of quaternionic right linear bounded operators, Linear and Multilinear Algebra, 70, 22 (2022) https://doi.org/10.1080/03081087.2021.1999382.

[11] V. Muller, Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras, 2nd edn. Birkhauser, Basel, 2007.

[12] W. Rudin, Functional Analysis, international Series in Pure and Applied Mathematics Vol.25 (First ed) New York (1973).

<footnote n="1">¹ Cadi Ayad University,
Marrakech, Morocco</footnote>

<footnote n="2">² Cadi Ayad University,
Marrakech, Morocco</footnote>
Luh hypercyclic vectors for composition
operator

**Communication Info**

**Authors:**

Noureddine Karim

Otmane BENCHIHEB

Mohamed AMOUCH

Chouaib Doukkali

University, El jadida,
Morocco

**Keywords:**

(1) Hypercyclicity

(2) composition operator

**Abstract**

For a function phi which is holomorphic on Omega, We deal with the construction of holomorphic functions f on Omega such that f and all its derivatives and antiderivatives under Cphi have dense orbit, which will be called a Luh hypercyclic vector for Cphi. We show that there is a dense linear manifold of Luh hypercyclic vectors.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Luh, W. (1988). Holomorphic monsters. Journal of approximation theory, 53(2), 128-144.

[2] Grosse-Erdmann, K. G., Mortini, R. (2009). Universal functions for composition operators with non-automorphic symbol. Journal d'Analyse Mathématique, 107, 355-376.

[3] Karim, N., Benchiheb, O., Amouch, M. (2024). Disjoint strong transitivity of composition operators. Collectanea mathematica, 75(1), 171-187.
Fuzzy Mathematics and LSTM for time series forecasting

**Communication Info**

**Authors:**

Yassine LAARICHI¹

Oualid RHOULAM¹

¹ University Ibn Tofail, Kenitra
Morocco

**Keywords:**

(1) Fuzzy logic

(2) Time series prediction

(3) LSTM networks

**Abstract**

varies approaches has been put forward for time series forecasting, from statistics to neural networks[1], and data transformations [2]. However, conventional models struggle with the inherent imperfections of historical data, which can be noisy or incomplete [3]. This study explores a new approach for timed series prediction, combining fuzzy logic with machine learning to improve forecast accuracy. The findings demonstrate the value of fuzzy mathematics in financial time series analysis, with broader implications for stock market and economic modeling.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] B. Lim and S. Zohren, "Time-series forecasting with deep learning: a survey," Philosophical Transactions of the Royal Society A, vol. 379, no. 2194, 2021, Art. no. 20200209.

[2] Y. Laarichi, M. Elkaf, A. Aloui, and O. Rholam, "Transforming data with the arcsine distribution for random walks," Mathematical Models in Engineering, vol. 10, no. 2-10, 2024. DOI: 10.21595/mme.2024.24105.

[3] R. P. Masini, M. C. Medeiros, and E. F. Mendes, "Machine learning advances for time series forecasting," Journal of Economic Surveys, vol. 37, no. 1, pp. 76-111, 2023.
**Communication Info**

**Authors:**

Salma RAIOUADI¹

Mohamed EL ALAOUI TALIBI²

Mouna HILAL³

¹ UCA, FSSM, Ibn Al Banna
Laboratory of Mathematics
and Applications (LIBMA),
Marrakech, Morocco

² UCA, FSSM, Ibn Al Banna
Laboratory of Mathematics
and Applications (LIBMA),
Marrakech, Morocco

³ UCA, FPS, Laboratory of
Modeling and Combinatorics
(LMC), Safi, Morocco

**Keywords:**

(1) Optimization

(2) Navier

(3) Fast algorithm

**Abstract**

In this work, we study cavitation and slip boundary problems for lubricated sliding contacts. The cavitation is modeled by the conservative compressible approach based on a non linear density-pressure relationship. The applied slip boundary condition is the Navier slip model, where the wall velocity is proportional to shear rate. Improving the performance of mechanical devices has always been a concern in mechanical engineering. The goal of this study is to find the optimal zone that maximizes the load capacity, defined as the integral of the pressure, which is obtained by solving the compressible Reynolds equation. We study the existence and uniqueness of the solution to the compressible Reynolds equation and prove the existence of an optimal solution. 1D simulations using a fast algorithm and a genetic algorithm, reveal optimal lubrication configurations, compared with previous work.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] G. Bayada, "A fast algorithm for boundary slippage including mass flow conserving cavitation model," *Tribology International*, **118**, 2018, pp. 71-88.

[2] G. Bayada, M. El Alaoui Talibi, M. Hilal, "Optimum design for slip/no-slip configuration of hydrodynamic fluid film using Gradient method," *Preprint*, 2024, DOI: 10.21203/rs.3.rs-5159215/v1.
Existence criteria for fractional sequential
hybrid integro-differential equations with
tempered ψ-Caputo operators

**Communication Info**

**Authors:**

Walid BENHADDA¹
Abderrazak KASSIDI¹
Ali EL MFADEL¹
M'hamed ELOMARI¹

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

**Keywords:**

(1) Hybrid differential
equation

(2) Tempered ψ-fractional
integral

(3) Tempered ψ-Caputo
fractional derivative

**Abstract**

The aim of this paper is to investigate the existence
results for two types of fractional hybrid integro-
differential equations involving tempered ψ-Caputo
fractional operators. The existence of solutions is
established using Dhage's fixed point theorem for three
operator equations in a Banach algebra and a
generalized Krasnoselskii fixed point theorem. Finally,
two illustrative examples are given to verify our
theoretical results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Dhage, B. C., On a fixed point theorem in Banach algebras with applications, Appl. Math. Lett., 18, (2005), 273-280.

[2] Mali, A. D., Kucche, K. D., Fernandez, A., and Fahad, H. M., On tempered fractional calculus with respect to functions and the associated fractional differential equations, Math. Methods Appl. Sci. 45, (2022), 11134-11157.

[3] Medved, M., and Pospisil, M., Generalized Laplace transform and tempered ψ-Caputo fractional derivative, Math. Model. Anal., 28, (2023), 146-162.

[4] Zhao, Y., Sun, S., Han, Z., and Li, Q., Theory of fractional hybrid differential equations, Comput. Math. Appl. 62, (2011), 1312-1324.
## Hyers-Ulam Type Stabilities of Iterative Integro-Differential Equations of High Order

### Communication Info

**Authors:**

Merve SENGUN OGUZ¹

Cemil TUNC 2

¹ Van Yuzuncu Yil University,
Van - Turkey

² Van Yuzuncu Yil University,
Van - Turkey

**Keywords:**

(1) Hyers-Ulam Stability

(2) Hyers-Ulam-Rassias
Stability

(3) Iterative Integro-
Differential Equation

### Abstract

In this study, we establish sufficient conditions of Hyers-Ulam stability, Hyers-Ulam-Rassias stability and -semi-Hyers-Ulam stability for an iterative Volterra integro-differential equation of higher order. Using fixed point method, Bielecki metric, etc., we prove new three theorems regarding the iterative Volterra integro-differential equation of higher order. The results of this study provide new, extensive and improved contributions to the qualitative theory of integro-differential equations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

### References

[1] Castro, L. P., Ramos, A., Hyers-Ulam and Hyers-Ulam-Rassias stability of Volterra integral equations with delay. Integral methods in science and engineering. Vol. 1, 85-94. Birkhäuser Boston, Ltd., Boston, MA, 2010.

[2] J.R. Graef, C. Tunç, M. Şengün, O. Tunç, The stability of nonlinear delay integro-differential equations in the sense of Hyers-Ulam. Nonauton. Dyn. Syst. 10 (2023), vol. 10, no. 1, 2023, pp. 20220169.

[3] Kucche, K. D., Shikhare, P. U., Ulam stabilities via Pachpatte's inequality for Volterra-Fredholm delay integro-differential equations in Banach spaces. Note Mat. 38 (2018), no. 1, 67-82.

[4] A. M. Simões, F. Carapau, P. Correia, New Sufficient Conditions to Ulam Stabilities for a Class of Higher Order Integro-Differential Equations. Symmetry. 2021; 13(11):2068.

[5] M. Şengün, C. Tunç, New results of Ulam stabilities of functional differential equations of first order including multiple retardations. Appl. Appl. Math. 18 (2023), no. 2, Art. 4, 15 pp

[6] O. Tunç, C. Tunç, On Ulam stabilities of iterative Fredholm and Volterra integral equations with multiple time-varying delays. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 83 (2024), 20 pp.
# Choquard-Kirchhoff problems involving variable exponents depending on the solution

**Communication Info**

**Authors:**

Noureddine Moujane¹
Mohamed El Ouaarabi¹,²
Said Melliani¹

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

² Faculty of Sciences Ain Chock, Hassan II University, Casablanca, Morocco

**Keywords:**

(1) Musielak-Orlicz Sobolev space

(2) Choquard-Kirchhoff problems

(3) Topological degree methods

**Abstract**

In this paper, we establish the existence of weak solutions to Choquard-Kirchhoff-type problems involving a double-phase operator, where the exponents depend on the solution. Such problems arise in various areas of applied mathematics and physics, providing a flexible framework that is well-suited for modeling complex systems, such as the flow of non-Newtonian fluids through porous media, phase transitions, and fluid dynamics.

By employing the topological degree theorem, we prove the existence of weak solutions for the considered problem within the framework of Musielak-Orlicz-Sobolev spaces under appropriate assumptions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Antontsev, S. Shmarev, On a class of nonlocal evolution equations with the $p[u(x, t)]$-Laplace operator, Nonlinear Anal. Real World Appl. 56 (2020), 103165.

[2] R. Arora, A. Fiscella, T. Mukherjee, P. Winkert, Existence of ground state solutions for a Choquard double phase problem. *Nonlinear Analysis, Real World Applications*. 73 (2023), 103914.

[3] Zeidler, E.: Nonlinear Functional Analysis and its Applications II/B. Springer-Verlag, New York, (1990).
<figure><img src="image_64.png" /></figure>

# Minimizing Fractional Programs by Blocks

**Communication Info**

**Authors:**

Chimaa ENNOURI¹

Ahmed ROUBI ¹

Karima BOUFI ²

¹ Faculty of Sciences and
Technologies, Settat, Morocco

² Higher Institute of Health
Sciences, Settat, Morocco

**Keywords:**

(1) Fractional Programming

(2) Dinkelbach's Algorithm

(3) Block Coordinate Descent
Method

**Abstract**

We are interested in solving optimization problems, known as fractional programs, whose objective function is defined as the ratio of two real-valued functions defined on $ℝ^n$. This type of problems is difficult to solve since they are generally non-convex, and become more difficult when their size n is very large. For this, we combine two methods to solve them: Dinkelbach's algorithm, which transforms the fractional problem into a sequence of simpler (convex) subproblems defined by a parameter, and the Block Coordinate Descent algorithm which divides the variables into blocks and solves the problems by successively optimizing with respect to each block of variables while keeping the other blocks fixed. These two methods reduce the overall problems complexity and optimize their resolution.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Crouzeix, Jean-Pierre, Jacques A. Ferland, and Hien Van Nguyen. "Revisiting Dinkelbach-type algorithms for generalized fractional programs", Opsearch 45.2 (2008): 97-110.

[2] Crouzeix, J. P., J. A. Ferland, and S. Schaible. "An algorithm for generalized fractional programs", Journal of Optimization Theory and Applications 47.1 (1985): 35-49.

[3] Tseng, Paul. "Convergence of a block coordinate descent method for nondifferentiable minimization", Journal of optimization theory and applications 109 (2001): 475-494.
**Communication Info**

**Authors:**

Oumaima Bouaoultaine¹

Maryem El Karchani²

Nadia Idrissi Fatmi³

¹,²,³ ENSAK, Sultan Moulay Slimane University, Beni Mellal, Morocco

**Keywords:**

(1) Psoriasis

(2) Psoriatic arthritis

(3) Type 2 Diabetes

(4) Cardiovascular health

(5) Optimal controls

(6) Pontryagin's maximum principle

(7) Numerical simulations

**Abstract**

In this study, we present a novel mathematical model that describes the dynamics of psoriasis and psoriatic arthritis. The main objective is to mitigate the associated risks to cardiovascular health and type 2 diabetes through control strategies based on three key factors: patient awareness programs, medical follow-up, and the promotion of a healthy and consistent lifestyle. We prove the existence of optimal controls and characterize them using state variables and adjoint functions, relying primarily on Pontryagin's maximum principle. Numerical simulations under various scenarios highlight the effectiveness of the proposed optimization approach.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] The National Psoriasis Foundation. Psoriasis Foundation. December 2022. Available from: https://www.psoriasis.org/. [2] Authors, Title Journal, Volume, Year, Pages.

[3] Garshick MS, Ward NL, Krueger JG, Berger JS. Cardiovascular risk in patients with psoriasis: JACC review topic of the week. J Am Coll Cardiol. 2021;77(13):1670-80. doi: 10.1016/j.jacc.2021.02.009.

[4] Verywell Health. How prevalent is type 2 diabetes? Statistics and facts. February 06, 2023. Available from: https://www.verywellhealth.com/type-2-diabetes-statistics-5214216.

[5] Grigorenko NL, Grigorieva EV, Roi PK, et al. Optimal control problems for a mathematical model of psoriasis. Comput Math Model. 2019;30:352-63. doi: 10.1007/s10598-019-09461-y.
**Communication Info**

**Authors:**

Ahmed RIKOUNE¹

Mohamed LAGHDIR 2

¹ Department of Mathematics,
Faculty of Sciences, Ibn Zohr
University, B.P. 8106, Agadir,
Morocco

² Department of Mathematics,
Faculty of Sciences, Chouaib
Doukkali University, BP. 20, El
Jadida,
Morocco

**Keywords:**

(1) Multiobjective fractional programming

(2) Bilevel programming

(3) Conjugate duality

(4) Approximate optimality conditions

**Abstract**

In this paper, we establish necessary and sufficient approximate optimality conditions and some duality results of approximate proper efficient solutions for a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using a parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P<sup>µ</sup>) with µ ∈ ℝ<sup>p</sup>, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the ε-weak duality and ε-strong duality results for (P<sup>µ</sup>) are presented. These results permit us to give dual characterizations for the approximate proper efficient solutions to the problem (P).

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Aboussoror and S. Adly, A Fenchel-Lagrange duality approach for a bilevel programming problem with extremal-value function, J. Optim Theory Appl, 149, 2011, 254-268.

[2] A.M. Geoffrion, Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22, 1968, 618-630.

[3] M.H. Kim, G.S. Kim, G.M. Lee, On ε-optimality conditions for multiobjective fractional optimization problems, Fixed Point Theory Appl. 6, 2011, 1-13.

[4] B. Kohli, Sequential optimality conditions for multiobjective fractional programming problems, J. Math. Sci. 8, 128, 2014.

[5] J.C. Liu, ε-properly efficient solutions to nondifferentiable multiobjective programming problems, In Lecture Notes in Economics and Mathematical Systems, 12, 1999, 109-113.

[6] A. Rikouane, Optimality and duality for a weakly efficient solution of bilevel multiobjective fractional programming problems with extremal-value function, Rend. Mat. Appl. 45, 2024, 181-199.

[7] H. Wang, R. Zhang and E. Vargyas, Duality for Multiobjective Bilevel Programming Problems with Extremal-Value Function, J. Math. Res. Appl. 35, 2015, 311-320.
**Communication Info**

**Authors:**

Naima MEFTAH¹

Mohamed AMOUCH ²

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

**Keywords:**

(1) Tumor growth

(2) Dystrophin protein

(3) Stability analysis

(4) Lyapunov function

(5) Numerical simulations

**Abstract**

In this research work, the authors present a mathematical model to study the biological interplay between tumor growth, dystrophin protein, and the impact of age of onset and staging through a system of ordinary differential equations (ODEs). An area that has not been thoroughly explored in mathematical biology. Initially, a simplified model examines the interplay between dystrophin and tumor growth, with analytical and numerical solutions verifying stability at equilibrium points. Subsequently, a more intricate model factoring in the age of onset and staging is developed, and stability is again demonstrated via analytical and numerical methods. In the final phase, a three-dimensional model is introduced, and the Picard-Lindelof theorem confirms the existence and uniqueness of solutions. Stability analysis demonstrates conditional stability at the equilibrium points. The Lyapunov function is used for global stability analysis to confirm that the system follows a predictable, stabilizing trajectory rather than being chaotic or oscillatory. Numerical simulations, executed using the fourth-order Runge-Kutta method, support the analytical results numerically as well as graphically.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Padder, A., Qureshi, S., Dubey, R. S., Rather, M. u. D., & Afroz, A. (2025). Dynamical analysis of tumor-dystrophin interaction model with impact of age of onset and staging. *Fixed Point Theory and Algorithms for Sciences and Engineering*, 2025, Article number: 4.
<figure><img src="image_65.png" /></figure>

# Qualitative analysis of a SEIR epidemic model in spatially heterogeneous environment

## Communication Info

**Authors:**

Oualid Bahouh¹

Aziz Ouhinou ²

Khalil Ezzinbi³

¹ University Sultan Moulay Slimane, Beni Mellal, Morocco.

² University Sultan Moulay Slimane, Benimellal, Morocco.

³ Faculty of Sciences Semlalia, Marrakech, Morocco.

**Keywords:**

SEIR model.

Epidemic reaction-diffusion model.

Logistic source.

Endemic equilibrium.

## Abstract

Our aim in this work to study a diffusive SEIR epidemic model with a saturated incidence rate[1], a logistic growth rate for susceptibles, and Holling type II treatment in a spatially heterogeneous environment. We first analyze some fundamental properties of the parabolic system, including the uniform upper bound of solutions, the global stability of the disease-free equilibrium (DFE), uniform persistence, and the existence of endemic equilibria. Our numerical analysis supports the theoretical framework, demonstrating that the DFE is asymptotically stable under a stronger condition than R_0<1.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Xiao, Dongmei, and Shigui Ruan. "Global analysis of an epidemic model with nonmonotone incidence rate." *Mathematical biosciences* 208.2 (2007): 419-429.
**Communication Info**

**Authors:**

Siham HACHOUM¹

Imane EL BERRAI¹

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

**Keywords:**

(1) Epidemic model

(2) Time delay

(3) Incubation period

**Abstract**

Plants play an essential role in sustaining life on Earth, yet they are susceptible to diseases that can escalate into epidemics, threatening crop yields and food security. This study presents a deterministic mathematical model to simulate the dynamics of a wheat epidemic, focusing on rust - a prevalent fungal disease affecting wheat crops globally.

This disease is characterized by a latency period during which the pathogen invades host cells, reproduces, and spreads within the plant. his latency influences the speed of symptom onset and the extent of disease proliferation. To accurately capture this time-dependent aspect of disease progression, we introduced delays into the model, resulting in a system of delay differential equations (DDEs). We analyzed the dynamics of this DDE system, focusing on equilibria and stability to understand the effects of delayed transmission within the plant. Finally, we compared the numerical solutions of the original ordinary differential equations (ODEs) with those of the DDEs to illustrate how the introduction of delays influences disease dynamics.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Hachoum, M. Riouali, I. Elberrai, Mathematical Modeling and Optimal Control of Wheat STRIPE RUST disease, Adv. Math. Models Appl, 2024.

[2] J. E. Van Der Plank, Plant Diseases: Epidemics and Control, Edition 3, Academic Press, 1963.

[3] A. Huppert, G. Katriel, Mathematical modelling and prediction in infectious disease epidemiology, Clin Microbiol Infect 19(11), 999-1005.

[4] T. Erneux, Applied Delay Differential Equations, Springer, New York, 2009.
On the A-contractions operators

**Communication Info**

**Authors:**

Kenza GOUACH<fnref n="1" />

Hamid EZZAHRAOUI <fnref n="2" />

**Keywords:**

(1) A-contraction

(2) A-isometry

(3) Contraction

**Abstract**

The class of operators T acting on a hilbert space H
relative to a positive operator A on H and satisfying
T*AT ≤ A, is called A-contractions that generalizes the
well-known contractions, one of the most studied and
understood classes of operators, we'll try to take it as
the starting point for our study.

Even there are differences between the two classes , our
work on A-contractions operators is based on extending
some properties of contractions. As it was possible for
the classical Nagy-Foiaş-Langer and von Neumann-Wold
decompositions, we will try to give the generalization of
more decompositions for an A-contraction T, but this
would not be possible without specifying the
appropriate assumptions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] KUBRUSLY, Carlos S, An introduction to models and decompositions in operator theory, 1997.

[2] PAGACZ, Patryk, On Wold-type decomposition Linear algebra and its applications, Vol. 436, no 9, 2012, p. 3065-3071.

[3] SUCIU, Laurian, Canonical decompositions induced by A-contractions Note di Matematica, Vol. 28, no 2, 2010, p. 187-202.

[4] SUCIU, Laurian, Maximum subspaces related to A-contractions and quasinormal operators. Journal of the Korean Mathematical Society, Vol. 45, no 1, 2008, p. 205-219.

[5] SUCIU, Laurian, Some invariant subspaces for A-contractions and applications Extracta mathematicae, Vol. 21, no 3, 2006, p. 221-247.

<footnote n="1">¹Mohammed V university
Faculty of sciences, Rabat,
Morocco</footnote>

<footnote n="2">² Mohammed V university
Faculty of sciences, Rabat,
Morocco</footnote>
# Beamforming Optimization techniques for 6G Networks: Approaches and Perspectives

## Communication Info

**Authors:**

Mossaab ATZEMOURT ¹

Zakaria HACHKAR ¹

Younes CHIHAB ²

¹ Cadi Ayyad University,
Polydisciplinary Faculty, Safi,
Morocco

² Faculty of Sciences, Ibn Tofail
University, Kenitra, Morocco

**Keywords:**

(1) Beamforming Optimization

(2) Sixth-generation (6G)

(3) Machine learning algorithms

(4) Intelligent reflective surfaces

(5) Reconfigurable intelligent surfaces

## Abstract

Beamforming plays a key role in the evolution of sixth-generation (6G) wireless communication systems by optimizing signal transmission and reception [1]. This paper explores advanced approaches proposed in the literature to improve the efficiency of beamforming in complex and highly mobile environments, focusing on three major challenges: energy optimization, dynamic adaptability and interference mitigation. Key solutions include intelligent reflective surfaces [2], deep reinforcement learning [3], hybrid beamforming [4] and machine learning algorithms [5]. These technologies enable real-time adjustment of beams, improved network coverage and efficient management of terahertz band constraints. Reconfigurable intelligent surfaces [6], in particular, optimize wave reflection for targeted interference management and improved spectral efficiency. Together, these innovations act as strategic levers to meet the requirements of 6G, including ultra-low latency, high device density and reliable connectivity, while ensuring sustainable energy consumption.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Da Silva Brilhante, D., Manjarres, J., Moreira, R., Veiga, L., Rezende, J., Müller, F., Klautau, A., Mendes, L., & Figueiredo, F. "A Literature Survey on AI-Aided Beamforming and Beam Management for 5G and 6G Systems." Sensors, vol. 23, no. 9, 2023, article 4359.

[2] Ihsan, A., Chen, W., Asif, M., Khan, W., Wu, Q., & Li, J. "Energy-Efficient IRS-Aided NOMA Beamforming for 6G Wireless Communications." IEEE Transactions on Green Communications and Networking, vol. 6, 2022, pp. 1945-1956.

[3] Fozi, M., Sharafat, A., & Bennis, M. "Fast MIMO Beamforming via Deep Reinforcement Learning for High Mobility mmWave Connectivity." IEEE Journal on Selected Areas in Communications, vol. 40, 2022, pp. 127-142.

[4] Yan, W., Hao, W., Huang, C., Sun, G., Muta, O., Gačanin, H., & Yuen, C. "Beamforming Analysis and Design for Wideband THz Reconfigurable Intelligent Surface Communications." IEEE Journal on Selected Areas in Communications, vol. 41, 2022, pp. 2306-2320.

[5] Geranmayeh, P., & Grass, E. "Machine Learning Based Beam Selection for Maximizing Wireless Network Capacity." IEEE Access, vol. 12, 2024, pp. 45176-45186.

[6] Tang, Z., Zhu, X., Zhu, H., & Xu, H. "Energy-Efficient Optimization Algorithm Based on Reconfigurable Intelligent Surface and Rate Splitting Multiple Access for 6G Multicell Communication System." IEEE Internet of Things Journal, vol. 11, 2024, pp. 2097-2108.
# Logistic Growth and Relapse in the Stochastic Dynamics of SIRI Epidemics

**Communication Info**

**Authors:**

Mouad ESSEROUKH ¹

Adel SETTATI ¹

Aadil lahrouz ¹

¹ Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and Techniques, B.P. 416-Tanger Principale, Tanger, Morocco.

**Keywords:**

(1) Stochastic SIRI model

(2) Logistic growth

(3) Extinction of disease

**Abstract**

This paper develops a stochastic SIRI epidemic model that incorporates nonlinear relapse dynamics, logistic population growth, and a bilinear incidence rate. We begin by establishing the existence and uniqueness of a positive global solution, ensuring the model's well-posedness. Subsequently, we derive sufficient conditions that determine whether the disease will persist in the population or eventually become extinct. These theoretical results are rigorously analyzed and validated through numerical simulations, which illustrate the interplay between key model parameters and epidemic outcomes. Our findings provide valuable insights into the complex dynamics of infectious diseases with relapse and population regulation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Settati, A., Lahrouz, A., Assadouq, A., El Fatini, M., El Jarroudi, M., Wang, K. (2020). The impact of nonlinear relapse and reinfection to derive a stochastic threshold for SIRI epidemic model. Chaos, Solitons Fractals, 137, 109897.

[2] Harchaoui, B., Boutouil, S., Settati, A., Lahrouz, A., El Idrissi, M., $\&$ El Jarroudi, M. (2024). Stochastic SIRI epidemic model with global incidence rate and relapse. International Journal of Applied and Computational Mathematics, 10(6), 179.

[3] Aznague, S., El Idrissi, M., Brahim, A. N., Harchaoui, B., Boutouil, S., Settati, A., ... $\&$ El Amrani, J. (2023). A probabilistic SIRI epidemic model incorporating incidence capping and logistic population expansion. Appl. Math, 17(5), 773-789.

[4] J. Li, Z. Teng, G. Wang, L. Zhang, C. Hu, Stability and bifurcation analysis of an SIR epidemic model with logistic growth and saturated treatment, Chaos, Soliton. Fract. 99 63-71 (2017).

[5] El Fatini, M., Lahrouz, A., Pettersson, R., Settati, A., Taki, R. (2018). Stochastic stability and instability of an epidemic model with relapse. Applied Mathematics and computation, 316, 326-341.
ON A CLASS OF GENERALIZED P(X)-BIHARMONIC PROBLEM
WITH NO-FLUX BOUNDARY CONDITION

**Communication Info**

**Authors:**

Khalid Soualhine<fnref n="1" />
Mohamed Talbi <fnref n="2" />
Najib Tsouli<fnref n="1" />

**Keywords:**

(1) p(x)-biharmonic operator.

(2) No-flux boundary
condition.

(3) Weak solutions.

**Abstract**

Using variational methods, we obtain in this work, the multiplicity of nontrivial weak solutions for a class of generalized p(x)-biharmonic problem involving two nonlocal terms and two real parameters with indefinite weight under no flux boundary condition. The novelty here can be seen as a generalization and continuation to some existing results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Soualhine, K., Filali, M., Talbi, M., Tsouli, N.: A critical p(x)-biharmonic Kirchhoff type problem with indefinite weight under no-flux boundary condition, Bol. Soc. Mat. Mex. 28, 22(2022).

[2] Boureanu, M.M., Radulescu, V.D., Repovs, D.: On a p(.)-biharmonic problem with no-flux boundary condition, Comput. Math. Appl. 72(9), 2505-2515(2016).

[3] Kefi, K., Radulescu, V.D.: On a p(x)-biharmonic problem with singular weights, Z. Angew. Math. Phys., 68(4), Art. 80, 13 pp (2017).

[4] Miao, Q.: Multiple Solutions for Nonlocal Elliptic Systems Involving p(x)-Biharmonic Operator, Mathematics. 7(8), 756(2019).

<footnote n="1">¹ University of Mohammed I,
Oujda, Morocco</footnote>

<footnote n="2">² CRMEF, Oujda, Morocco.</footnote>
<figure><img src="image_66.png" /></figure>

# Height of Reed-Muller Codes: A Computational
Study

**Communication Info**

**Authors:**

Saber DARMOUN¹
Khalid ABDELMOUMEN ²
Hussain BEN-AZZA³

¹ Sidi Mohamed Ben Abdellah
University, Ecole Normale
Supérieure, Fez, Morocco

² Sidi Mohamed Ben Abdellah
University, Ecole Normale
Supérieure, Fez, Morocco

³ Moulay Ismail University,
ENSAM, Meknes, Morocco

**Keywords:**

(1) Reed-Muller Codes

(2) Power of a code

(3) Height of a linear code

**Abstract**

The theory of error-correcting codes is essential in the field of communication, particularly for ensuring the reliability of information transmission. Among the most well-known families of codes, Reed-Muller codes play a key role in error correction and optimization of communication system performance. These codes are widely used in applications such as data storage and wireless communication. In this study, we focus on the notion of the power of a linear code, as defined in reference [1], and the Height of an error-correcting code. The main objective of our work is to explore the power of classical and q-ary Reed-Muller codes and determine their associated heights. We generate a large number of examples using a computational software. This approach has not only deepened our understanding of the properties of Reed-Muller codes but has also raised new questions that may enrich the field of linear codes research. Our results pave the way for further discussion on the extension of this study to other families of codes.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. DARMOUN, K.ABDELMOUMEN, H.BEN-AZZA, Gulf Journal Of Mathematics (GJOM), Vol. 18, 2024, 29-46.

[2] T.KASAMI, SHU LIN, W.PETERSON, IEEE Transactions on Information Theory, Vol. 14, 1968, 189-199.

[3] T.KASAMI, N.TOKURA, IEEE Transactions on Information Theory, Vol. 16, 1970, 752-759.

[4] F. J MacWilliams, N. J. A Sloane, The theory of error-correcting codes, Vol. 16, Elsevier, 1977.

[5] A. SERGUEI, STEPANOV, Codes on Algebraic Curves, Springer Science and Business Media, 2012.
**Communication Info**

**Authors:**

Asmaa Baihi¹

Hamid Lmou¹

Khalid Hilal¹

Ahmed Kajouni¹

¹ Laboratory of Applied

Mathematics and Scientific

Computing, Sultan Moulay

Slimane University, Beni

Mellal, Morocco.

**Keywords:**

(1) $\psi$-Caputo fractional derivative;

(2) Volterra integral operator; generalized Laplace transform method; Banach's fixed point theorem;

(3) Hyers–Ulam stability

**Abstract**

In this paper, we deal with the coupled system of For Volterra integrodifferential equations of order (p,q), we use the generalized Laplace transform method to find the solution and obtain results on uniqueness using Banach's fixed point theorem. Next, we examine different stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, a concrete application is given to illustrate the effectiveness of our main results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Ali, M.R., Hadhoud, A.R. and Srivastava, H.M. Solution of fractional Volterra-Fredholm integro-differential equations under mixed boundary conditions by using the HOBW method. Adv Differ Equ 2019, 115 (2019).

[2] Alomari, A.-K.; Alaroud, M.; Tahat, N.; Almalki, A. Extended Laplace Power Series Method for Solving Nonlinear Caputo Fractional Volterra Integro-Differential Equations. Symmetry 2023, 15, 1296..

[3] Amin, M.B.M.; Ahmad, S.S. Laplace Transform for Solving System of Integro-Fractional Differential Equations of Volterra Type with Variable Coefficients and Multi-Time Delay. Symmetry 2022, 14, 984.

[4] Baihi, A., Kajouni, A., Hilal, K. et al. Laplace transform method for a coupled system of $(p, q)$-Caputo fractional differential equations. J. Appl. Math. Comput. (2024)..
<figure><img src="image_67.png" /></figure>

Hyers-Ulam Stability Analysis of Some Third-Order
Linear Differential Equations with Constant Coefficients

**Communication Info**

**Authors:**

Karim FARHAT¹
Idriss ELLAHIANI¹
Omar AJEBBAR¹
Belaid BOUIKHALENE²

¹Polydisciplinary Faculty,
Sultan Moulay Slimane
university, Beni Mellal,
Morocco

²National School of Applied
Sciences, Sultan Moulay
Slimane university, Beni Mellal,
Morocco

**Keywords:**

(1) Hyres-Ulam stability

(2) Differential equation

**Abstract**

This paper examines the Hyers-Ulam stability of the
third-order linear differential equation

$$
(E) : y^{(3)}(x) + (\delta - 2)y''(x) - (2\delta - 1)y'(x) + \delta y(x) = 0, \text{ for all } \epsilon > 0
$$

Where $\delta$ is a real parameter and [a,b] is a real interval.
A fundamental question in stability theory is whether
approximate solutions of differential equations remain
close to exact solutions under small perturbations. In
this context, we establish that if a function $f$ satisfies the
inequality

$$
|f^{(3)}(x) + (\delta - 2)f''(x) - (2\delta - 1)f'(x) + \delta f(x)| \le \epsilon, \text{ for all } \epsilon > 0
$$

then there exists an exact solution $y$ of equation (E)
such that

$$
|y(x) - f(x)| \le K\epsilon
$$

Where K is the Hyers-Ulam stability constant.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] C. Alsina, R. Ger, On some inequalities and stability results related to the exponential function, J. Inequal. Appl. 2 (4) (1998) 373-380.

[2] D.H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941) 222-224.

[3] Y. Li, Y. Shen, Hyers-Ulam stability of linear differential equations of second order?. March 2010 Applied Mathematics Letters 23(3):306-309.

[4] M. Onitsuka, T. Shoji, Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient, Applied Mathematics Letters 63 (2017) 102-108

[5] S.M. Ulam, A Collection of Mathematical Problems, Interscience Publ., New York, 1961. Problems in Modern Mathematics, Wiley, New York, 1964.
<figure><img src="image_68.png" /></figure>

# Generalized solution of transport equation in
Colombeau algebra using fixed point

**Communication Info**

**Authors:**

Soukaina SADEK
M'hamed ELOMARI
Abdellah TAQBIBT

Faculty of Sciences and
technologies,
University of Sultan Moulay
Slimane, Beni Mellal, Morocco

**Keywords:**

(1) Generalized solution

(2) Transport equation

(3) Colombeau algebra

(4) Fixed point theorem

(5) Association

**Abstract**

In this paper, we investigate the existence and uniqueness of the generalized solution for an important class of transport equations within the framework of Colombeau algebra G. Our approach relies on the application of the fixed-point theorem, combined with specific computational techniques to handle nonlinear initial conditions in the time variable t. Furthermore, we establish a connection between the classical and generalized solutions of the transport equation, highlighting the consistency of our approach within the Colombeau algebraic setting. Our results contribute to a deeper understanding of generalized functions in the context of partial differential equations with singularities or irregular data.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] S. Sadek, L. S. Chadli, A. Moujahid, M. Elomari, S. Melliani, Filomat, Vol 38, 2024, 589-597.

[2] J.F. Colombeau, North-Holland Math.Stud, 1985, 113.

[3] M. Oberguggenberger, Pitman Res. Notes Math. Ser., 1992, 259.

[4] J. F. Colombeau, North Holland, Amsterdam/New York/Oxford, 1984

[5] M. Oberguggenberger and M. Kunzinger, Mathematische Nachrichten, no. 1, 1999, 147-157.

[6] H. Deguchi and M. Oberguggenberger, J. Fixed Point Theory Appl. 2020.

[7] Mohamed Chaib, Abdellah Taqbibt, M'hamed El Omari, Said Melliani, Int. J. Appl. Comput. Math, 2025.

[8] Khalid Latracha, M. Aziz Taoudib, Ahmed Zeghal, J. Differential Equations, 2006, 256-271.

[9] M. Boumhamdi, K. Latrach, A. Zeghal, J.Math 16, 2016, 3155-3171.
**Communication Info**

**Authors:**

Abdelali OUFKIRI¹

Tarek ZARI ²

¹ Hassan II University of Casablanca / Faculty of Legal, Economic and Social Sciences Ain Sebaa, Casablanca, Morocco

² Hassan II University of Casablanca / Faculty of Legal, Economic and Social Sciences Ain Sebaa, Casablanca, Morocco

**Keywords:**

(1) supply chain management

(2) green management

(3) overall performance

**Abstract**

Green Supply Chain Management (GSCM) is increasingly recognized as a strategic approach to enhancing firms' overall performance by integrating environmental considerations into supply chain operations [1]. In the context of Moroccan industrial firms, the adoption of GSCM practices aims to improve operational efficiency and strengthen social legitimacy [2]. This study employs Structural Equation Modeling (SEM) to examine the impact of internal environmental practices on firms' overall performance. The findings reveal a significant positive relationship between internal GSCM practices and performance improvement [3]. However, the extension of environmental practices to external stakeholders, such as suppliers and customers, does not yield a significant performance boost [4]. These results highlight the importance of internal environmental initiatives in achieving sustainability goals and competitive advantage [5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**Reference**

[1] Srivastava, S. K. (2007). Green supply-chain management: A state-of-the-art literature review. *International Journal of Management Reviews*, 9(1), 53-80.

[2] Sarkis, J., Zhu, Q., & Lai, K. H. (2011). An organizational theoretic review of green supply chain management literature. *International Journal of Production Economics*, 130(1), 1-15.

[3] Green, K. W., Zelbst, P. J., Meacham, J., & Bhadauria, V. S. (2012). Green supply chain management practices: Impact on performance. *Supply Chain Management: An International Journal*, 17(3), 290-305.

[4] Geng, R., Mansouri, S. A., & Aktas, E. (2017). The relationship between green supply chain management and performance: A meta-analysis of empirical evidences in Asian emerging economies. *International Journal of Production Economics*, 183, 245-258.

[5] Zhu, Q., Sarkis, J., & Lai, K. H. (2008). Confirmation of a measurement model for green supply chain management practices implementation. *International Journal of Production Economics*, 111(2), 261-273.
On the Optimization of Control Flow Graphs:
Algorithmic and Computational Perspectives

**Communication Info**

**Authors:**

M. Hafid 1*

S. Abdelalim 2

I. Elmouki 2

D. Karim 1

* Meryemh553@gmail.com

1 Faculty of Sciences and
Techniques of Mohammed,
University Hassan II of
Casablanca, Morocco.

2 Faculty of Sciences Ain
Chock, University Hassan II of
Casablanca, Morocco.

**Keywords:**

(1) Control Flow Graph

(2) DGCNNs

(3) Artificial Intelligence

(4) Software defect

**Abstract**

After analyzing the fundamental properties of Control Flow Graphs (CFGs), we focus on their structural refinement through formal algorithmic methods. Simplifying CFGs is essential for improving program analysis, particularly in areas such as software verification and defect detection. More importantly, we explore how CFG transformations enhance the effectiveness of Dynamic Graph Convolutional Neural Networks (DGCNNs) in predicting software defects. By refining CFG structures while preserving key control dependencies, we enable more expressive graph-based representations for learning-based approaches.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Wu, L., Cui, P., Pei, J., Zhao, L., & Guo, X., Graph neural networks: foundation, frontiers and applications. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, (2022, August). (pp. 4840-4841).

[2] Corso, G., Stark, H., Jegelka, S., Jaakkola, T., & Barzilay, R., Graph neural networks. Nature Reviews Methods Primers, 4(1), 17, (2024).

[3] Liu, Z., & Zhou, J., Introduction to graph neural networks. Springer Nature, (2022).

[4] Phan, A. V., Le Nguyen, M., Nguyen, Y. L. H., & Bui, L. T., Dgcn: A convolutional neural network over large-scale labeled graphs. Neural Networks, 108, (2018), 533-543.
An equilibrium vectorial version
of Borwein-Preiss's variational principle

**Communication Info**

**Authors :**

DOUHOU ABDESSAMAD
MAADEN ABDELHAKIM

Faculté des Sciences et Techniques,
Beni Mellal, Maroc

**Keywords:**

(1) Variational principles

(2) Vector equilibrium problems

(3) Quasi-metric spaces

(4) Gerstewitz's functional

**Abstract**

In this work, we investigate in vector optimization problems where functions map from a quasi-metric space to a vector space that may or may not be endowed with a topological structure. We propose an extended algebraic vectorial version of lower semicontinuity, inspired by topological setting, and discribe it in terms of the closedness of level sets. The primary contribution of this work is the to present a vectorial equilibrium form of the Borwein-Preiss variational principle, as discussed in [5], by establishing the existence of solutions for perturbed equilibrium problems. To do this, we use a nonlinear scalarization approach by applying some algebraic properties of the Gerstewitz's functional [3,4]. In a particular case, a vectorial form of an Ekeland-type variational principle for bifunctions will be deduced.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] ANSARI, Qamrul Hasan, KÖBIS, Elisabeth, et YAO, Jen-Chih. *Vector variational inequalities and vector optimization*. Cham: Springer International Publishing AG, 2018.

[2] Borwein, Jonathan M., and David Preiss. "A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions." Transactions of the American Mathematical Society, **303**(2), 1987, 517-527.

[3] Gutiérrez, César, et al. "Nonconvex separation functional in linear spaces with applications to vector equilibria." SIAM Journal on Optimization, **26**(4), 2016, 2677-2695.

[4] Gutiérrez, César, et al. "Ekeland variational principles in vector equilibrium problems." SIAM Journal on Optimization, **27**(4), 2017, 2405-2425.

[5] Yongxin, Li, and Shi Shuzhong. "A generalization of Ekeland's $\varepsilon$-variational principle and its Borwein-Preiss smooth variant." Journal of mathematical analysis and applications, **246**(1), 2000, 308-319.
Topological degree for an
anisotropic equation with variable growth

**Communication Info**

**Authors:**

Hamza JOURHMANE <fnref n="1" />
Abderrazak KASSIDI <fnref n="1" />
M'hamed ELOMARI <fnref n="1" />
Khalid HILAL <fnref n="1" />

**Keywords:**

(1) Topological degree

(2) Periodic solution

(3) Dirichlet conditions

(4) Generalized Sobolev spaces

(5) Anisotropic $p(x, t)$-Laplacian

(6) Variable growth

**Abstract**

The idea behind the present paper is to establish the existence of a periodic non-negative solution for a degenerate parabolic equation [2] with anisotropic $p(x, t)$-Laplacian operator [3] and strongly nonlinear source under Dirichlet type boundary conditions [4]. This will be approached by a proof based on the Leray-Schauder topological degree [1], which can be challenging to work with in this type of equations as well as the blow up argument [5].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Abbassi, C. Allalou, and A. Kassidi, Existence of weak solutions for nonlinear $p$-elliptic problem by topological degree. Nonlinear Dyn. Syst. Theory, 20(3), (2020), 229-241.

[2] Authors, Title Journal, Volume, Year, Pages.

[3] J. Chen, Z. Zhang, G. Chang and J. Zhao. Periodic Solutions to Klein-Gordon Systems with Linear Couplings. Adv. Nonlinear Stud. 2021; 21(3): 633-660.

[4] H. Jourhmane, A. Kassidi, M. Elomari and K. Hilal, Existence of periodic solution for double-phase parabolic problems with strongly nonlinear source. Filomat 37:27 (2023), 9357-9370.

[5] V.V. Zhikov, On some variational problems, Russ. J. Math. Phys. 5 (1) (1997) 105-116.

<footnote n="1">¹ Faculty of sciences and
techniques, Beni Mellal,
Morocco</footnote>
<figure><img src="image_69.png" /></figure>

# The global existence of the stochastic Quasi-geostrophic equations in Fourier-Besov-Morrey

## Communication Info

**Authors:**

Hassan Khaider¹
Mohamed El Ouaarabi ²
Abderrahmane Raji¹

¹ Faculty of Science and
Technology of Beni Mellal,
Sultan Moulay Slimane
University, Beni Mellal.

2 Faculty of Sciences Aïn
Chock, Hassan II University,
Casablanca.

**Keywords:**

(1) Itô integral.

(2) Stochastic Quasi-geostrophic equations.

(3) Fourier-Besov-Morrey
spaces.

## Abstract

This paper investigates the global well-posedness of solutions for the two-dimensional stochastic Quasi-Geostrophic (SQG) equation in Fourier-Besov-Morrey spaces. By employing the Itô integral, we establish the existence and uniqueness of global mild solutions under suitable assumptions on the initial data and the external random forcing term. For comparison, we also present corresponding results for the deterministic case. The analysis leverages tools from harmonic analysis, including Littlewood-Paley theory and Fourier-Besov-Morrey spaces, which are well-suited for handling the regularity and scaling properties of the equation. Using a fixed-point approach and stochastic estimates, we derive precise conditions ensuring the well-posedness of the SQG equation in this critical functional framework. Our results extend previous studies on deterministic quasi-geostrophic equations by incorporating stochastic forcing, thereby contributing to the understanding of randomness in geophysical fluid models.equation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] M. Z. Abidin, J. C. Chen; Global well-posedness of generalized magnetohydrodynamics equations in variable exponent Fourier-Besov-Morrey spaces, \emph{Acta Math. Sin. (Engl. Ser.)}, \textbf{38} (2022), 2187–2198.

[2] A. Azanzal, C. Allalou, S. Melliani; Well-posedness and blow-up of solutions for the 2D dissipative quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces, \emph{J. Elliptic Parabolic Equ.}, \textbf{8} (2022), 849–872.

[3] H. Bae; Global well-posedness of dissipative quasi-geostrophic equations in critical spaces, \emph{Proc. Amer. Math. Soc.}, \textbf{136} (2008), 257–261.

[4] M. Cannone; A generalization of a theorem by Kato on Navier-Stokes equations, \emph{Rev. Mat. Iberoam.}, \textbf{13} (1997), 515–541.
# A Novel Dynamic Threshold Approach for Image Restoration

## Communication Info

**Authors:**

Abdelghafour ATLAS¹

Jamal ATTMANI¹

Fahd KARAMI²

¹LMSC, Cadi Ayyad University,
ENSA Marrakech, Morocco

²MIMSC, Cadi Ayyad University,
EST Essaouira, Morocco

**Keywords:**

(1) Image Processing

(2) Perona-Malik Equation

(3) Dynamical threshold

## Abstract

This study presents a mathematical and numerical analysis of a novel image denoising model. The model is developed by combining the H-1-norm decomposition approach with a dynamic threshold-based Perona-Malik (DTPM) method. By incorporating a dynamic threshold function into the edge indicator, the model adaptively adjusts the diffusion mode and strength based on the image's characteristics. Using Schauder's fixed point theorem, we prove the existence and uniqueness of weak solutions for the proposed model. Finally, numerical experiments and comparative analyses are conducted to demonstrate the model's effectiveness and performance.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Li, Q., Hu, Y. and Cao, Y., 2023. Adaptive Perona-Malik model based on dynamical threshold for image multi-noise removal with details preservation. *Computers & Mathematics with Applications*, **137**, pp.28-43.

[2] L. Afraites, A. Atlas, F. Karami, D. Meskine, Some class of parabolic systems applied to image processing, Discrete & Continuous Dynamical Systems-B 21, no. 6 (2016): 1671.

[3] Z. Guo, J. Yin, Q. Liu, On a reaction-diffusion system applied to image decomposition and restoration, Math. Comput. Modelling, **53** (2011), no. 5-6, 13361-1350.
Points algébriques de degrés au-plus 5 sur la
courbe $C$ d'équation affine $y^2 = 3(x^5 - 1)$

**Communication Info**

**Authors:**

El Hadji SOW¹

Oumar SALL ²

¹ Université Assane SECK,
Ziguinchor, Sénégal

² Université Assane SECK,
Ziguinchor, Sénégal³

**Keywords:**

(1) Courbes planes

(2) Degré d'un point

(3) Points rationnels

(4) Extentions algébriques

(5) Jacobienne

**Abstract**

Dans ce travail, nous déterminons l'ensemble des points
algébriques de degrés au-plus 5 sur $\mathbb{Q}$ sur la courbe
$C$ d'équation affine : $y^2 = 3(x^5 - 1)$.

L'énoncé obtenu étend un résultat de Siksek qui a décrit
dans [3] l'ensemble des points $\mathbb{Q}$-rationnels sur cette
courbe.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] P. A. Griffiths, Introduction to algebraic curves, Translations of mathematical monographs volume 76. American Mathematical Society, Providence, 1989.

[2] O. Sall, Points algébriques sur certains quotients de courbes de Fermat, C. R. Acad. Sci. Paris Ser. I 336, 2003, 117-120.

[3] S. Siksek, Explicit Chabauty over number fields, Algebra & Number Theory, Volume 7, 2013, No. 4, page 765-793.

[4] L.C. Washington, Elliptic curves, Number Theory and Cryptography, Second Edition, 2008.
Sequential efficiency optimality conditions for a robust
multiobjective fractional optimization problems

**Communication Info**

**Authors:**

M'hamed MABROUK¹

Mohamed LAGHDIR²

Ahmed ED-DAHDAH³

¹,²,³Department of
Mathematics, Faculty of
Sciences, Chouaib Doukkali
University, BP. 20, El Jadida,
Morocco

**Keywords:**

(1) Conjugate function

(2) Efficiency solution

(3) Robust multiobjective
fractional optimization

(4) Optimality conditions

**Abstract**

The aim of this paper is to establish, without any
constraint qualification, sequential optimality
conditions for a vector constrained robust
multiobjective fractional programming problem,
characterizing an efficient solution. This is achieved in
terms of the epigraphs of the conjugate, approximate
subdifferential, and the subdifferential of the involved
functions at the minimizer. Finally, we present an
example illustrating the main results of this paper.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] A. Ben-Tal, L. El Ghaoui, A. Nemirovski, Robust Optimization, Princeton Series in Applied Mathematics, 2009.

[2] A. Ben-Tal, A. Nemirovski, Robust optimization-methodology and applications, Math, Program, Ser, B 92, 2002, 453-480.

[3] S.S. Manesh, M. Saraj, M. Alizadeh, M. Momeni, On robust weakly ε-efficient solutions for multi-objective fractional programming problems under data uncertainty, AIMS Math, 7, 2021, 2331-2347.

[4] X.K. Sun, X.J. Long, Y. Chai, Sequential optimality conditions for fractional optimization with applications to vector optimization, J Optim Theory Appl, 164, 2015, 479-499.

[5] M.B. Moustaid, M. Laghdir, I. Dali, A. Rikouane, Sequential optimality conditions for multiobjective fractional programming problems via sequential subdifferential calculus, Le Matematiche, 76, 2021, 79-96.
<figure><img src="image_70.png" /></figure>

Regularized generalized canonical correlation
analysis for multiblock data analysis

Communication Info

Authors:

Hanane ZAHRAOUI<fnref n="1" />,<fnref n="2" />
Zouhair EL HADRI <fnref n="1" />
Mohamed HANAFI<fnref n="2" />
Mohamed ZIANI<fnref n="1" />

Keywords:

(1) Multiblock datasets

(2) RGCCA

(3) Regularization

(4) High-dimensional data

Abstract

This paper explores multiblock data analysis different
methods, where the variables are separated into distinct
blocks measured on the same individuals.
We focus here on a special and powerful framework for
exploring complex, high-dimensional and multicollinear
datasets, called Regularized canonical correlation
analysis (RGCCA) [1].

RGCCA is used to uncover relationships across different
data blocks [2], but it requires experts to define the
links between them in advance [3], a step that can be
challenging and could influence both the analysis and
the results.

In this paper, we aim to demonstrate the flexibility and
practical utility of RGCCA through real-world
applications, where we illustrate the flexibility and
practical value of RGCCA, emphasizing its ability to
provide stable and reliable insights while achieving
strong goodness of fit [4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] Arthur Tenenhaus, Michel Tenenhaus, Psychometrika, 76 (2), 2011, pp. 257-284.

[2] Tenenhaus, Arthur & Tenenhaus, Michel, Elsevier, 238 (2), 2014, 391-403.

[3] Stéphanie Bougeard, Statistics [stat]. Université Rennes 2, 2019.

[4] H. D. Vinod, Econometrica, 25 No.2, 1968, pp. 322-336.

<footnote n="1">¹ Faculty of sciences, Rabat,
Morocco</footnote>

<footnote n="2">² ONIRIS, Nantes, France</footnote>
**Communication Info**

**Authors:**

Amal EZZIDANI<fnref n="1" />

Mohamed GHAZALI<fnref n="1" />

Othmane EL MOIZE<fnref n="2" />

**Keywords:**

(1) batches arrivals

(2) single server breakdowns

(3) embedded Markov chains

**Abstract**

In this paper, we consider a batch arrival $M^{[X]}/M/1$ queue model with single server breakdowns and the sizes of successive arriving batches being independent and identically distributed random variables. For this model, we analyze a two-dimensional Markov chain and give its quasi-upper triangle transition probability matrix. Under the system stability condition, we derive the steady-state probabilities, and then obtain the expressions of the various performance measures of the queueing system. Finally, some numerical examples are given to illustrate the effect of the parameters on the system performance measures.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Neuts, Marcel F. *Structured stochastic matrices of M/G/1 type and their applications*. CRC Press, 2021.

[2] Rider, Kenneth Lloyd. "A simple approximation to the average queue size in the time-dependent M/M/1 queue." *Journal of the ACM (JACM)* 23, no. 2, 1976, pp 361-367.

[3] Latouche, Guy, and Vaidyanathan Ramaswami. *Introduction to matrix analytic methods in stochastic modeling*. Society for Industrial and Applied Mathematics, 1999.

[4] Liu, Zaiming, and Yang Song. *The M[X]/M/1 queue with working breakdown, RAIRO-Operations Research* 48, no. 3, 2014, p 399-413.

[5] Sudhesh, Ramupillai, and Arumugam Vaithiyanathan. *Stationary analysis of infinite queueing system with two-stage network server, RAIRO-Operations Research* 55, 2021, pp S2349-S2357.

<footnote n="1">¹ FSTS, Settat, Morocco</footnote>

<footnote n="2">² ENSA, Tetouan, Morocco</footnote>
Approximate weak and proper subdifferentials of the
difference of two vector convex mappings and applications

**Communication Info**

**Authors:**

Ahmed ED-DAHDAH¹

Mohamed LAGHDIR²

M'hamed MABROUK³

Abdelghali Ammar⁴

¹,²,³Department of
Mathematics, Faculty of
Sciences, Chouaïb Doukkali
University, BP. 20, El Jadida,
Morocco

⁴Department of Computer
Engineering, Networks and
Telecommunications, National
School of Applied Sciences,
9 Cadi Ayyad University, Safi,
Morocco

**Keywords:**

(1) Approximate Pareto
subdifferential

(2) DC programming

(3) Vector optimization

(4) Optimality conditions

**Abstract**

In this paper, we provide a general formula concerning the weak and proper approximate subdifferentials of the difference of two vector convex mappings (DC) in terms of the star difference. This formula is applied to establish necessary and sufficient approximate optimality conditions, characterizing weakly and properly approximate efficient solutions for a constrained DC programming problem and a constrained multiobjective fractional programming problem.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] N. Gadhi, A. Metrane, Sufficient optimality condition for vector optimization problems under D.C. data, J. Global Optim. 28, 2004, 55-66.

[2] X. Guo, S. Li, Optimality conditions for vector optimization problems with difference of convex maps, J. Optim. Theory Appl. 162, 2014, 821-844.

[3] A. Taa, Optimality conditions for vector optimization problems of a difference of convex mappings, J. Glob. Optim. 31, 2005, 421-436.

[4] M. El Maghri, M. Laghdir, Pareto subdifferential calculus for convex vector mappings and applications to vector optimization, SIAM J. Optim. 19, 2008, 1970-1994.

[5] A. Ammar, M. Laghdir, A. Ed-dahdah, M. Hanine, Approximate subdifferential of the difference of two vector convex mappings, Mathematics 11, 2023, 2718.
Comparing Penalized and Random Effects
Quantile Regression Models for Longitudinal Data

**Communication Info**

**Authors:**

Fatima Zahra AHSOUS(a)

Hasna CHAMLAL(a)

Karim OULKACHA(b)

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

(b) 201, Ave Président-Kennedy
H2X 3Y7, Montreal, Quebec,
Canada

**Keywords:**

(1) Quantile regression

(2) Longitudinal data

(3) Random effects

(4) Penalty methods

(5) Asymmetric Laplace
distribution

**Abstract**

In traditional mixed models, longitudinal data analysis relies on Gaussian random effects models. However, this assumption does not provide enough flexibility to handle heterogeneous individual effects. We present two linear quantile regression models for longitudinal data, one incorporates L_1 regularisation to manage the individual fixed effects [1], and the other includes random effects using the Asymmetric Laplace Distribution [2] to account for the dependence between repeated measurements within the same subject. The first method applies L_1 regularization to shrink individual fixed effects and uses Sparse linear algebra and interior point methods to efficiently solve the large scale optimization problem. The second model uses the Asymmetric Laplace Distribution to estimate quantile regression parameters and uses likelihood ratio tests to evaluate the significance of the parameters. The results show that models effectively selects optimal shrinkage level for individual effects, outperforms penalized fixed effects approaches and provides a robust alternative to mean regression with random effects for skewed longitudinal data. Regularization significantly reduces estimation variability and handles a large number of fixed effects.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Koenker, R. (2004). Quantile Regression for Longitudinal Data. Journal of Multivariate Analysis, 91(1), 74-89.

[2] Geraci, M., Bottai, M. (2007). Quantile Regression for Longitudinal Data Using the Asymmetric Laplace Distribution. Biostatistics, 8(1), 140-154.
Multiplicity of solutions for fractional (p, q)-Laplacian equations involving the critical exponents and Hardy potential in R<sup>N</sup>

**Communication Info**

**Authors:**

Rachid ECHARGHAOUI¹

Rachid SERSIF¹

¹ Ibn Tofail university, Kenitra, Morocco

**Keywords:**

(1) Fractional (p,q)-Laplacian

(2) Critical point theorem.

(3) Variational methods,

**Abstract**

In this paper, we study a fractional (p,q)-Laplacian equation with critical exponent exponents and Hardy potential in R<sup>N</sup>. By using an abstract critical point theorem from [4] and by employing the concentration compactness principle of Lions, we obtain a multiple solutions for β sufficiently large. A similar problem with subcritical exponents is also considered.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Alves, C.O., da Silva, A.R.: Multiplicity and concentration behavior of solutions for a quasilinear problem involving N-functions via penalization method. Electron. J. Differ. Equ. 2016(158), 1–24. (2016)

[2] Di Nezza, E., Palatucci, G., Valdinoci, E.: Hitchhiker's guide to the fractional sobolev spaces. Bulletin des Sciences Mathématiques. 136(5), 521–573. (2012)

[3] Lions, P.L.: The concentration-compactness principle in the calculus of variations. The limit case. I. Rev. Mat. Iberoamericana. 1, 145–201. (1985)

[4] Perera, K.: Abstract multiplicity theorems and applications to critical growth problems. J. Anal. Math.(in press) (2023)
Li-Yorke chaotic C0-semigroup

**Communication Info**

**Authors:**

Halima HASSANI¹

Mohamed AMOUCH ²

¹ University Chouaib Doukkali,
El Jadida, Morocco

² University Chouaib Doukkali,
El Jadida, Morocco

**Keywords:**

(1) Li-Yorke chaos

(2) Hypercyclicity

(3) C0-semigroups

**Abstract**

A strongly continuous semigroup (shortly C₀-semigroup) (T_t)_{t \geq 0} on a Banach space X is said to be Li-Yorke chaotic if it admits an uncountable scrambled set. In this talk, we will review some results regarding Li-Yorke chaos for C₀-semigroups. Also, we will introduce and study a generalization of this class of C₀-semigroups, providing necessary and sufficient conditions for this new class. Additionally, we will explore the connections between this notion and other existing concepts in linear dynamics. At the end of the talk, we will present several examples to illustrate these ideas.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Amouch, M., Bachir, A., Benchiheb, O., Mecheri, S.: Weakly recurrent operators. Mediterr. J. Math. 20:169(2023).

[2] N.C. Bernardes Jr., A. Bonilla, V. Muller, A. Peris, Li-Yorke chaos in linear dynamics, Ergodic Theory Dynam. Systems, 35 (6) (2015) 1723-1745.

[3] M. Kostic, Li-Yorke chaotic properties of abstract differential equations of first order, Appl. Math. Comput. Sci. 1 (2016), 15–26.

[4] .Zhang, X. Chen, G. R. Linear Li-Yorke chaos in a finite-dimensional space with weak topology, Int.J. Bifurcation and Chaos 31, No. 14, (2021).
Threshold Dynamics of an Hiv Reactivation Model with Latent
Infection, Macrophages, Logistic Growth, and Distributed Delay

**Communication Info**

**Authors:**

Hanane HMARRASS¹
Redouane QESMI²

¹ LMSM, Department of
Mathematics, Sidi Mohamed
Ben Abdellah University,
Faculty of Science and
Technology, Fez, Morocco

² LMSM, Department of
Mathematics, Sidi Mohamed
Ben Abdellah University,
Higher school of Technology,
Fez, Morocco

**Keywords:**

(1) HIV

(2) logistic growth

(3) Distributed Delay

(4) Hopf Bifurcation.

**Abstract**

To better understand the within-host dynamics of viral
infections, including HIV, we develop an age-structured
model that captures interactions between the virus and
two distinct cell populations. This model incorporates a
latent reservoir in the second compartment, a loss term
in the free virus equation, and a logistic growth term for
healthy cells. Using the method of characteristics, we
reduce the system to a set of differential equations with
distributed delay. A comprehensive mathematical
analysis is conducted, including stability and bifurcation
analysis, to identify key factors influencing disease
progression. We determine the basic reproduction
number, which dictates whether the infection persists or
is eradicated. Furthermore, we establish sufficient
conditions for the local and global asymptotic stability of
the disease-free equilibrium and identify bistability
phenomena. By examining the endemic equilibrium
through a fourth-order exponential polynomial
characteristic equation, we detect Hopf bifurcations on
both the forward and upper branch of the backward
bifurcation. Finally, numerical simulations validate the
theoretical findings.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Hmarrass H, Qesmi R, Global stability and Hopf bifurcation of a delayed HIV model with macrophages, CD4+T cells with latent reservoirs and immune response. EPJ, 2025(Accepted).

[2] Hmarrass H, Qesmi R, Stability and backward bifurcation for an HIV model with macrophages and CD4+T cells with latent reservoirs. MATCOM, 2024; 225:370-395. https://doi.org/10.1016/j.matcom.2024.05.026.
**Communication Info**

**Authors:**

BOUMAAZA TOURIA
AMOUCH MOHAMED
BENCHIHEB OTMANE

Chouaib Doukkali

University, Faculty of
science El Jadida, Morocco.

**Keywords:**

(1) Recurrent

(2) R-mixing

(3) interval map

**Abstract**

An operator T acting on a metric compact space X is said to be recurrent if, for each nonempty open subset U of X, there exists $n \in N$ such that $T^n(U) \cap U \neq \emptyset$. In this paper, we introduce and study the notion of recurrence of interval map. We investigate some properties of this class of operators and show the links between recurrence, R-mixing and weakly R-mixing of operators and interval maps.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Ruette, Sylvie. Chaos on the interval, University Lecture Series, 67. American Mathematical Society, Providence, RI (2017): 1-3.

[2] Costakis, George, Antonios Manoussos, and Ioannis Parissis. Recurrent linear operators. Complex Analysis and Operator Theory 8 (2014): 1601-1643

[3] Furstenberg, Harry. Recurrence in ergodic theory and combinatorial number theory. Vol. 10. Princeton University Press, 2014.

[4] Grosse-Erdmann, Karl-G., and Alfred Peris Manguillot. Linear chaos. Springer Science Business Media, 2011.

[5] Bès, Juan, et al. "Recurrence properties of hypercyclic operators." Mathematische Annalen 366 (2016): 545-572
<figure><img src="image_71.png" /></figure>

# Applications of discrete moments in image watermarking

**Communication Info**

**Authors:**

Chaimae CHEKIRA<fnref n="1" />

Hakim EL FADILI <fnref n="2" />

**Keywords:**

(1) Discrete moments

(2) Watermarking

(3) Reconstruction

**Abstract**

Discrete moments are an effective frequency features for describing the visual content of an image. They have thus been widely and successfully applied in various fields of technical research [1], as they offer a number of advantages, including high image representation capacity while minimizing computational complexity. In addition, they enable near-perfect reconstruction of the original image with low error and high robustness against noise. In particular, image moments are useful in watermarking applications [2], as they minimize image reconstruction error after data hiding in the moment domain while guaranteeing quality watermark extraction even in the presence of attacks. The following study presents the most known orthogonal moments in different coordinate spaces (cartesian and polar) and their application into image watermarking [3].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] I. Batioua, R. Benouini, and K. Zenkouar, "Image recognition using new set of separable three-dimensional discrete orthogonal moment invariants," Multimedia Tools Appl., vol. 79, nos. 19-20, May 2020, pp. 13217-13245.

[2] M. Alghoniemy and A. H. Tewfik, "Image watermarking by moment invariants," in Proc. Int. Conf. Image Process., vol. 2. Vancouver, BC, Canada: IEEE, 2000, pp. 73-76.

[3] C. Chekira, M. Marzouq, I. Batioua, H.E. Fadili, Z. Lakhliai, K. Zenkouar, New blind image moments watermarking method based on evolutionary optimization of embedding parameters, IEEE Access 11, 2023, 48517-48547.

<footnote n="1">¹ LIPI, USMBA, Fez, Morocco</footnote>

<footnote n="2">² LIASSE, USMBA, Fez, Morocco</footnote>
<figure><img src="image_72.png" /></figure>

On The Rank of a Subfamily of Elliptic
Curves Extracted From $E(t): y^2 = x^3 - (a + bt)x$

**Communication Info**

**Authors:**

KOUAKOU Kouassi Vincent

Université Nangui ABROGOUA,

Côte d'Ivoire

**Keywords:**

(1) Elliptic Curves

(2) Independence

(3) Rank

(4) Specialization

(5) Generators

(6) Birationally equivalent to

**References**

[1] J. Aguirre, A. Dujella an J.C. Peral, On the rank of elliptic curves coming from rational Diophantine triples, Rocky Mountain J. Math. 42 (2012), 1759-1776.

[2] A. Brumer, The average rank of elliptic curves I, Invent. Math. 109 (1), 445-472, 1992.

[3] J.W.S. Cassels, Diophantine equations with special reference to elliptic curves, J. London. Math. Soc. 1 (1), 193-291, 1966.

[4] A. Choudhry, Symmetric diophantine systems and families of elliptic curves of high rank, Rocky Mountain J. Math. 49 (2019), 1419-1447.

[5] I. Cornnell, Elliptic Curves Handbook. 1999.

**Abstract**

We extract an infinity subfamily

$$E(k): y^2 = x^3 + (k^2 - 1)x$$

of elliptic curves from the curve

$$E(t): y^2 = x^3 - (a + bt)x.$$

Then, by imposing, successively, points on the obtained curves $E(k)$, we increase the rank. At the end, we show that its rank is at least 3 over $\mathbb{Q}(h)$.

[6] N. D. Elkies, Three lectures on elliptic surfaces and curves of high rank, arXiv. 0709 [math.NT] 18 sep 2007

[7] N. D. Elkies and Z. Klagsbrun, New rank records for elliptic curves having rational torsion, The Open Book Series 4 (2020) Fourteenth Algorithmic Number Theory Symposium https://doi.org/10.2140/obs.2020.4.233

[8] A. Dujella and J.C. Peral, High rank elliptic curves with torsion $\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/4\mathbb{Z}$ induced by Diophantine triples, LMS J. Comput. Math. 17 (2014), 282-288.

[9] M. v. Hoeij, An algorithm for computing the Weierstrass normal form, ISSAC'95- 7/95 Montreal, Canada, 1995, 90-95.

[10] F. Izadi, A. S. Zargar, A Note on Twists, Iranian Journal of Mathematical Sciences and Informatics, Vol. 12 (1), 2017, 27-34.

[11] Magma Calculator Version V 2:28-19, Available online at: http://magma.maths.usyd.edu.

[12] Maple 18; Available online at: https://www.maplesoft.com

[13] B. Mazur. Modular curves and the Eisenstein ideal. Publications Mathématiques de l'Institut des Hautes Études Scientifiques Vol 47.1 (1977): 33-186.

[14] J.-F. Mestre, Construction d'une courbe elliptique de rang $\ge 12$, C. R. Acad. Sci. Paris Sér. I 295 (1982), 643-644.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700
# ON THE RESOLUTION OF THE LATTICE VECTOR PROBLEMS USING UNIMODULAR MATRICES

## Communication Info

**Authors:**

Mohammed-Yasser EZ-ZAHER
Seddik ABDELALIM
Chaymae ED-DYB
Ilias ELMOUKI

Faculté des sciences Ain
Chock, Université Hassan 2,
Casablanca

**Keywords:**

(1) Lattice reduction

(2) Orthogonalization

(3) Gram-Schmidt Process

(4) QR decomposition

(5) LLL algorithm

## Abstract

In this talk, we introduce a matrix scheme that uses a QR decomposition adjusted to the Gram-Schmidt orthogonalization process for the resolution of the lattice vector problems, using unimodular matrices. This matrix procedure enables us to guarantee the quasi-orthogonality between the desired vectors under a new inequality and even establish an updated condition on the basis reduction with respect to its size.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] A.K. Lenstra, H.W. Lenstra Jr., L. Lovász, Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515-534. 1982.

[2] M.R. Bremner. Lattice basis reduction: an introduction to the LLL algorithm and its applications. CRC Press. ISBN: 1439807027, 9781439807026, p.332, 2011
Uncertainty modelling of the nonlinear Black-Scholes
equation and decision-making using fuzzy logic

**Communication Info**

**Authors:**

Amal Aarab¹

Aicha Driouch²

¹ Hassan First University,
Berrechid, Morocco

² Cadi Ayyad University,
Marrakesh, Morocco

**Keywords:**

(1) Fuzzy logic

(2) Black-Scholes Equation

(3) *Nonlinear PDE*

(4) Decision-Making

**Abstract**

In the field of finance, particularly in option pricing, forecasting the value of underlying assets is challenging due to fluctuations in interest rates and volatility. To enhance prediction accuracy, a fuzzy-based approach [1] serves as a powerful tool for capturing the uncertainty inherent in financial markets. This study introduces a numerical method for pricing European options by employing a fuzzy-parameter partial differential equation [2]. We investigate the extended nonlinear Black-Scholes model proposed by Barles and Soner; studied numerically in [3,4] for the crisp case; enabling the computation of a range of European option prices. The fair price is determined using the center of gravity method [5], while the corresponding confidence level and confidence interval are obtained through an optimization process. These findings contribute to improved forecasting and decision-making in financial applications.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] L. A. Zadeh, Information and Control, 8, 1965, 338-353.

[2] T. Allahviranloo, Computational Methods in Applied Mathematics, De Gruyter Berlin, 2, 2002, 233–242.

[3] M. Abounouh, H. Al Moatassim, A. Driouch, & O. Goubet, Advances in Nonlinear Analysis, 9, 2020. 654-664.

[4] A. Driouch, & H. Al Moatassime, Annals of the University of Craiova-Mathematics and Computer Science Series, 47, 2020, 25-34.

[5] W. Van Leekwijck, E. E. Werner, Fuzzy Sets and Systems, Elsevier, 108, 1999, 159–178.
# Stochastic analysis of temporal tumor evolution with macrophage effects

**Communication Info**

**Authors:**

Abdelaziz BEN LAHBIB¹

Lahcen AZRAR¹

Ateq Ahmed AL-Ghmedi²

¹ Research Center STIS, M2CS, Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University, Rabat, Morocco.

² Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

**Keywords:**

(1) Stochastic Differential Equations

(2) Extinction and Persistence

(3) Tumor-macrophage

**Abstract**

This paper investigates the behavior dynamic of tumors with macrophage interaction. Stochastic analysis is elaborated under the environment noise in order to explore the impact of random fluctuations on the dynamics of the model. The deterministic analysis is also briefly done including stable and unstable limit cycles, period-doubling bifurcation under certain parameter conditions. Theoretical theory based on Lyapunov analysis method is elaborated to prove the existence of a unique positive solution and to determine sufficient condition for the persistence and extinction of tumor cells. Additionally, numerical simulations are elaborated to validate the theoretical findings and to observe the impact of noise in the Hopf bifurcation.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] BEN LAHBIB Abdelaziz, AZRAR Lahcen and BEN AMAR Martine, Stochastic modeling and analysis of interactions between cancer-associated fibroblasts and T-cell cytotoxic activity in tumor-immune system: the case of human lung tumors, Submitted to Applied Mathematical Modeling, 2025.

[2] EFTIMIE Raluca and BARELLE Charlotte. Mathematical investigation of innate immune responses to lung cancer: The role of macrophages with mixed phenotypes. *Journal of Theoretical Biology*, 2021, vol. 524, p. 110739.

[3] SHU Yaqin, HUANG Jicai, DONG Yueping, and al. Mathematical modeling and bifurcation analysis of pro-and anti-tumor macrophages. *Applied Mathematical Modelling*, 2020, vol. 88, p. 758-773.
<figure><img src="image_73.png" /></figure>

# Évaluation du système Ramed dans la ville d'Agadir :
## Modélisation par équations structurelles

## Communication Info

**Authors:**

Amine RADAH¹
Mohamed ELHIA²

¹ FSJES Ain Sebaa, Université
Hassan II, Casablanca, Maroc

² FSJES Ain Sebaa, Université
Hassan II, Casablanca, Maroc

**Keywords:**

(1) Modèle d'équations
structurelles (SEM)

(2) Système Ramed

(3) Sécurité sociale

## Abstract

Depuis 2021, le Maroc a entrepris une réforme historique en généralisant la couverture médicale pour l'ensemble de sa population, s'inscrivant dans un projet plus large de renforcement de la sécurité sociale. Cette initiative vise à garantir un accès universel aux soins de santé et marque une étape décisive dans les politiques sociales du pays, dans la continuité des efforts déjà engagés avec la mise en place du Régime d'Assistance Médicale (RAMED) en 2008. Ce programme, conçu pour offrir une couverture médicale aux citoyens économiquement démunis, est fondé sur des principes de solidarité, d'équité et d'inclusivité.

Malgré l'importance du RAMED dans l'élargissement de l'accès aux soins, le programme a rapidement montré ses limites. Les bénéficiaires ont dû faire face à des défis persistants, notamment des infrastructures médicales insuffisantes, des processus administratifs complexes, et des insuffisances dans la qualité des services. Ces problématiques soulèvent la question de l'adéquation du RAMED avec les besoins réels des populations cibles et appellent à une réflexion sur les améliorations nécessaires pour garantir l'efficacité de la couverture généralisée.

Cet article propose une évaluation novatrice du niveau de satisfaction des bénéficiaires du système RAMED dans la ville d'Agadir, une zone à forte densité de population et à diversité socio-économique marquée. En utilisant une modélisation par équations structurelles (SEM), nous identifions les facteurs clés qui influencent la perception de la population vis-à-vis de ce système. Cette recherche fournit des éléments empiriques précieux pour optimiser les politiques de santé et contribuer à la réussite du projet de généralisation de la couverture médicale, tout en consolidant la sécurité sociale pour l'ensemble de la population.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Akhnif, E., et al., *The place of learning in a universal health coverage health policy process: the case of the RAMED policy in Morocco*, (2019).

[2] Ferrie, J.-N., Omary, Z., & Serhan, O., Le Régime d'assistance médicale (RAMED) au Maroc : Les mécomptes du volontarisme et de l'opportunisme, (2022)

[3] Chin, W. W., & Newsted, P. R., *Structural equation modeling analysis with small samples using partial least squares.*, (1999).
<figure><img src="image_74.png" /></figure>

Adaptive Sampling-Enhanced PINNs for Improved
Thermal Modeling in Additive Manufacturing

**Communication Info**

**Authors:**

Idriss BARBARA¹

Tawfik MASROUR ¹,²

Mohammed HADDA ¹

1 ENSAM-Meknes, Moulay Ismail
University of Meknes, Morocco.

2 University of Quebec at
Rimouski, Rimouski, Canada.

**Keywords:**

(1) Physics-Informed Neural
Networks (PINN)

(2) Partial Differential Equations

(3) Adaptive sampling

(4) Thermal modeling

**Abstract**

Accurate thermal modeling is critical for ensuring the quality and structural integrity of additive manufacturing processes. While Physics-Informed Neural Networks (PINNs) [1] have emerged as a powerful tool for solving partial differential equations (PDEs) such as the heat equation, their performance is often hindered by the limitations of uniform or random sampling strategies [2]. I am working on introducing an adaptive sampling technique designed to boost the performance of PINN when addressing the heat equation in thermal modeling of additive manufacturing processes. Unlike traditional approaches that rely on uniform or random sampling, the method I present strategically focuses on regions with higher error estimates. The result is a more efficient training process and enhanced accuracy in temperature prediction. In this communication, I will outline the adaptive sampling strategy, share insights from its application, and discuss its potential impact on real-time thermal control and process optimization in additive manufacturing [3].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations. Journal of Computational Physics, 378, 686–707.

[2] Wang, S., Teng, Y., Li, H., & Karniadakis, G. E. (2022). When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics, 439, 110534.

[3] Liao, S., Xue, T., Jeong, J. et al. Hybrid thermal modeling of additive manufacturing processes using physics-informed neural networks for temperature prediction and parameter identification. Comput Mech 72, 499–512 (2023).
# Stabilization with decay estimate of distributed parameter second order systems by bilinear control damping

## Communication Info

**Authors:**

Khalil EL KAZOUI¹

Hassan Ezzaki²

¹Ibn zohr university, Agadir
Morocco

**Keywords:**

(1) Distributed Parameter
Systems

(2) Stabilization

(3) Decay estimate

## Abstract

This paper deals with stabilization and energy decay rates of second-order bilinear systems in a Hilbert space. Namely, we examine a class of bounded feedback control to investigate weak, strong, and exponential stabilization. Firstly, we discuss the well-posedness of mild solutions of the considered systems using the cosine family. Secondly, we provide some sufficient conditions to ensure feedback stabilization for the bilinear systems which are presented in terms of observation estimates. Moreover, we derive an explicit decay estimate of the energy in the case of strong stabilization. Finally, we offer examples with numerical simulations to demonstrate the applicability of our theoretical results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Khalil El Kazoui, Hassan Ezzaki, Abed Boulouz. Stabilization with decay estimate of infinite dimensional second order systems by bilinear control damping. Evolution Equations and Control Theory, 2025, 14(3): 494-510. doi: 10.3934/eect.2024065

[2] Ezzaki, L., & Zerrik, E. H. (2020). Stabilisation of second-order bilinear and semilinear systems. International Journal of Control, 94(12), 3483-3490. https://doi.org/10.1080/00207179.2020.1770335
Anticycling in Linear Problems with Big Data

**Communication Info**

**Authors:**

Asmaa AIT BRIK¹
Seddik Abdelalim ²
Ilias Elmouki ³
Tarik Yassir ⁴

¹,²,³,⁴ Faculty of Sciences Ain
Chock, University Hassan II of
Casablanca, Morocco

**Keywords:**

(1)Cycling problem

(2)Linear program

(3)Simplex method

(4)Anti-cycling

(5)Lexicography

(6)Bland's rule

**Abstract**

In this talk, we aim to discuss the cycling problem often met in the resolution of linear programs. In fact, if we take just the example of the simplex method, we could find ourselves in front of either an open loop or an infinite number of iterations due to the absence of non-degenerate bases. In order to avoid such issues in computation, we could refer for instance to two *anticycling* methods, namely *lexicography* and *Bland's* rule, and then we look for more advanced procedures that may be beneficial even for big data.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Minoux, M. (2008). *Programmation mathématique. Théorie et algorithmes*. Lavoisier.

[2] Bazaraa, M. S., Jarvis, J. J., & Sherali, H. D. (2011). Linear programming and network flows. John Wiley & Sons.

[3] Mordukhovich, B. S., & Nam, N. M. (2014). An easy path to convex analysis and applications (p. 2014).
*Williston*: Morgan & Claypool.
# Numerical Solution of Time-Dependent Heat Diffusion Problems Using an Enriched Finite Element Method

## Communication Info

**Authors:**

Ibrahim BASSIR¹

Boujemâa ACHCHAB ¹

Mohammed SEAID ²

¹ National School of Applied Sciences, Berrechid, Morocco

² School of Engineering and Computing Sciences, University of Durham, Durham, UK

**Keywords:**

(1) Finite Element Method
(FEM)

(2) Partition of Unity Method

(3) Time-Dependent Diffusion

(4) Generalized Finite Element
Method

## Abstract

We present a generalized finite element method, enriched by a partition of unity, for time-dependent diffusion problems.

This approach, which extends the traditional finite element method, incorporates multiple exponential functions to capture both spatial and temporal diffusion decay within the finite element space.

Compared to the conventional FEM, it is simpler, more efficient, and provides greater accuracy.

Numerical results confirm the method's efficiency and accuracy for transient diffusion equations.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] MELENK, Jens M. BABUSKA, Ivo, The partition of unity finite element method: basic theory and applications, Computer methods in applied mechanics and engineering, Vol. 139, 1996, P. 289-314.

[2] SHADI MOHAMED, M., SEAID, Mohammed, TREVELYAN, Jon, et al, A partition of unity FEM for time-dependent diffusion problems using multiple enrichment functions., International Journal for Numerical Methods in Engineering, Vol. 93, 2013, P. 245-265.

[3] IQBAL, Muhammad, GIMPERLEIN, Heiko, MOHAMED, M. Shadi, et al., An a posteriori error estimate for the generalized finite element method for transient heat diffusion problems., International Journal for Numerical Methods in Engineering, Vol. 110, 2017, P. 1103-1118.
Dynamics of a Two-Strain Epidemic Model in Complex network with Nonlinear Incidence rate and time delay

**Communication Info**

**Authors:**

Hakim HABRI

Amine El KOUFI ²

Brahim FAHID ³

¹ Ibn Tofail university, Kenitra,
Morocco

² Ibn Tofail university, Kenitra,
Morocco

³ Ibn Tofail university, Kenitra,
Morocco

**Keywords:**

(1) Complex networks

(2) Nonlinear incidence

(3) Global stability

**Abstract**

Motivated by [1, 2, 3], we proposed a new two-strain SIR epidemic model in heterogeneous complex networks with nonlinear incidence rate and two time delays. The model consists of four equilibrium points: the disease-free equilibrium, the strain 1 endemic equilibrium, the strain 2 endemic equilibrium and the both strains endemic equilibrium. We analyzed the global stability of these equilibrium points using suitable Lyapunov functions and LaSalle's invariance principle [4, 5]. Two basic reproduction numbers are found, $R_1$ and $R_2$. If $R_1 < 1$ and $R_2 < 1$, the disease die out. However, if either $R_1 > 1$ or $R_2 > 1$, the corresponding strain will persist, which leads to endemic state.

Finally, we performed numerical simulations on scale-free networks to validate our theoretical results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Kuddus, M. A., McBryde, E. S., Adekunle, A. I., & Meehan, M. T. (2022). Analysis and simulation of a two-strain disease model with nonlinear incidence. *Chaos, Solitons & Fractals, 155*, 111637.

[2] CHENG, Xinxin, WANG, Yi, et HUANG, Gang. Dynamics of a competing two-strain SIS epidemic model with general infection force on complex networks. *Nonlinear Analysis: Real World Applications*, 2021, vol. 59, p. 103247.

[3] LI, Chin-Lung, CHENG, Chang-Yuan, et LI, Chun-Hsien. Global dynamics of two-strain epidemic model with single-strain vaccination in complex networks. *Nonlinear Analysis: Real World Applications*, 2023, vol. 69, p. 103738.

[4] FALL, A., IGGIDR, Abderrahman, SALLET, Gauthier, et al. Epidemiological models and Lyapunov functions. *Mathematical Modelling of Natural Phenomena*, 2007, vol. 2, no 1, p. 62-83.

[5] LI, Jianquan, XIAO, Yanni, ZHANG, Fengqin, et al. An algebraic approach to proving the global stability of a class of epidemic models. *Nonlinear Analysis: Real World Applications*, 2012, vol. 13, no 5, p. 2006-
# Developing A Supervised Learning-Based Web
Application For Cancer Tumor Analysis

**Communication Info**

**Authors:**

Nouhaila HOUSSA¹
Seddik ABDELALIM²
Chaymae ED-DYB³
Ilyas ELMOUKI⁴

¹²,³,⁴LMFA Faculty of Sciences
Ain Chock, University Hassan II
of Casablanca, Morocco

**Keywords:**

(1) Breast cancer

(2) Flask framework

(3) React

(4) Machine Learning

(5) Supervised classification

(6) logistic regression

**Abstract**

One of the most prevalent cancers in women worldwide is breast cancer, and lowering mortality rates depends on early identification. Conventional diagnostic techniques mostly depend on clinical expertise, where errors in judgment or delays can significantly impact outcomes. The emergence of web technologies, machine learning, and contemporary frameworks such as Flask and React, present promising opportunities to assist with clinical decision-making. This project investigates the deployment of a Flask-React web application that uses cutting-edge machine learning algorithms to classify breast cancer as benign or malignant. In order to minimize pre-processing and guarantee robust performance, our classification introduces a logistic regression and trains it on clinical datasets. The Flask backend handles data processing and model inference, while the React frontend provides a dynamic and intuitive user interface, enabling healthcare professionals to input patient data and visualize classification results seamlessly.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Menard, S. W. (2010). Logistic regression: From introductory to advanced concepts and applications. Sage.

[2] Adedeji, O. (2023). Full-Stack Flask and React: Learn, code, and deploy powerful web applications with Flask 2 and React 18. Packt Publishing Ltd.
# Analysis of Anisotropic Interpolation Error in Sobolev Spaces with Applications to Mesh Optimization

## Communication Info

**Authors:**

Mohamed elhassan BASSIR¹

Boujemâa ACHCHAB ¹

Abdellatif AGOUZAL ²

¹ National School of Applied Sciences, Berrechid, Morocco

² Camille Jordan Institute, Lyon, France

**Keywords:**

(1) Anisotropic interpolation

(2) Mesh adaptation

(3) Finite element

## Abstract

We present results on anisotropic interpolation error for functions in Sobolev spaces, establishing explicit upper and lower bounds. The study focuses on sequences of conformal, anisotropic meshes in dimensions $d=2$ and $d=3$, using a metric based on the Hessian matrix. This metric controls the interpolation error by incorporating measurements of the volume and perimeter of the simplices. The goal is to guide the construction of quasi-optimal meshes that enhance both accuracy and computational efficiency. These results have applications in a posteriori error estimation and mesh adaptation strategies for solving partial differential equations using the finite element method.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Achchab. B, Agouzal. A, Majdoubi. A, Meskine. D, Souissi. A, A posteriori error analysis for nonconforming approximations of an anisotropic elliptic problem. Numer. Methods Part. Diff. Equ. 31(3), 659-976. (2015).

[2] Achchab. B, Laayouni. L, Polman. J and Souissi. A, Anisotropic A posteriori Error Estimations in convection-diffusion with Dominant Convection. Internat. J. Appl. Sc. Comput. 10(1), 11-29.(2003).

[3] Agouzal. A, On the saturation assumption and hierarchical a posteriori error estimator, CMAM 1 (1) 125 131.(2001).

[4] Agouzal. A, Lipnikov. K, Vassilevski. Yu, Anisotropic mesh adaptation for solution of finite element probems using hierarchical edge-based error estimates, in: B. Clark (Ed.), Proceedings of 18th International Meshing Roundtable, Springer, Salt Lake City, pp. 595-610.(2009).

[5] Agouzal. A, Lipnikov. K, Vassilevski. Yu, Hessian-free metric-based mesh adaptation via geometry of interpolation error, J. Comput. Math. Math. Phys. 50 124-138.(2010).
<figure><img src="image_75.png" /></figure>

Optimizing over the Weakly Efficient set of a
Multi-Objective Optimization Problem

Communication Info

Authors:

Zakia ANKHILI¹
Hanane HIMMI¹
Mohamed Oumoun¹

¹ National School of Applied
Sciences-Marrakesh,
Cadi Ayyad University,
Morocco

Keywords:

(1) multi-objective
optimization

(2) linear programming

(3) weakly efficient set

(4) penalty method

Abstract

Optimizing over the efficient set or the weakly efficient set of a multi-objective problem remains a challenging issue. The main reason is that the feasible set of our optimization problem is implicitly defined. Moreover, the efficient solution set is neither closed nor convex, even when all functions are linear. Identifying an efficient solution can therefore be difficult. To address this challenge, several advanced approaches have been proposed to find efficient solutions for nonlinear multi-objective optimization problems [1-4].

In this paper, we focus on studying a nonlinear multi-objective
optimization problem over the weakly efficient set of a linear
multi-objective optimization problem. We propose a penalty
method inspired by [5,6] to characterize the weakly efficient set
and prove that our problem can be reduced to solving a
sequence of multi-objective optimization problems with linear
constraints. Finally, we present an algorithm to solve this
problem.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

References

[1] H.P. Benson, 1984. Optimization over the efficient set. Journal of Mathematical Analysis and Applications 98, 560-580

[2] Banu Lokman and Murat Köksalan. Finding all nondominated points of multi-objective integer programs. Journal of Global Optimization, 57(2):347–365, 2013.

[3] Flores-Bazaan. F, Vera, C.: Efficiency in quasiconvex multiobjective nondifferentiable optimization on the real line. Optimization. 71(2), 285-307 (2022).

[4] Yamamoto, Y.: Optimization over the efficient set: overview. J. Glob. Optim. **22**, 285–317 (2002).

[5] z. Ankhili, Multiobjective Bilevel Optimization Problem : Penalty method, Internationa Conference on Learning and Optimization Algorithms : Theory and Applications, Rabat,2nd to 5th May 2018.

[6] Z. Ankhili and A. Mansouri, An exact penalty on bilevel programs with linear vector optimization lower level, 2009, European Journal of Operational Research, vol.197,36-41
# Stability and Numerical Results for Double Wall Carbon Nanotubes Modeled as Shear Beams

## Communication Info

**Authors:**

My Driss Aouragh<fnref n="1" />

El Alami Bouchra <fnref n="2" />

El Baz Mustapha<fnref n="2" />

M'hamed Segaoui <fnref n="2" />,<fnref n="3" />

Abdelaziz Soufyane <fnref n="4" />

**Keywords:**

(1) Shear beam

(2) Double Wall Carbon

Nanotubes

(3) Stabilization

## Abstract

We consider the one-dimensional equation for the double wall carbon nanotubes modeled by a coupled shear beam system with a distributed damping system. By applying the theory of semigroups of linear operators, we prove the well-posedness of the problem. We also demonstrate the exponential stabilization of the total energy of the system, with partial damping, without assuming equal wave velocities. Additionally, we analyze the fully discrete problem using the finite element method. We present the construction of numerical energy and simulations that demonstrate our theoretical exponential decay results.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Apalara, Tijani A., and Hassan A. Almutairi. "Well-posedness and stability of double wall carbon nanotubes Timoshenko system under Lord-Shulman thermoelasticity." Discrete and Continuous Dynamical Systems-S (2025)

[2] Apalara, Tijani A., and Kassimu Mpungu. Well-posedness and stability result for carbon nanotubes Timoshenko beams with second sound. Applicable Analysis: 1-16 (2024).

[3] Ramos, A. J., Rincon, M. A., Madureira, R. L., and Freitas, M. M. Exponential stabilization for carbon nanotubes modeled as Timoshenko beams with thermoelastic effects. ESAIM: Mathematical Modelling and Numerical Analysis, 57(3), 1171-1193 (2023).

[4] Sobrado Suárez, F. M., Barbosa Sobrado, L. D., de Araujo, G. L. L., and Rodrigues Mendes, F. B. Stability and regularity for double wall carbon nanotubes modeled as Timoshenko beams with thermoelastic effects and intermediate damping. Mathematical Methods in the Applied Sciences, 47(12), 10185-10213 (2024).

<footnote n="1">¹ EST, Moulay Ismail University
of Meknes, Morocco</footnote>

<footnote n="2">² FST Errachidia, Moulay
Ismail University of Meknes,
Morocco</footnote>

<footnote n="3">³ ENSIASD of Taroudant, Ibn
Zohr University, Morocco</footnote>

<footnote n="4">⁴ College of Sciences, University
of Sharjah, UAE</footnote>
<figure><img src="image_76.png" /></figure>

# Mathematical Model of Tumor Spheroid with Real-Time Cell Cycle and Physics-Informed

## Communication Info

**Authors:**

Hamza AGUEDJIG<fnref n="1" />
Sidi Mohamed DOUIRI <fnref n="1" />
Imad EL HARRAKI<fnref n="2" />
Mohammed EL HAMMANI<fnref n="1" />

**Keywords:**

(1) Modeling

(2) Tumor

(3) Neural network

(4) Cell Cycle

## Abstract

This work is part of the ongoing advancements in mathematical modeling of tumor growth using mathematical equations. What sets this study apart from previous works is its integrative approach, which aims to establish a connection between the theoretical foundations inherited from past research and contemporary technological and scientific advancements. First, our study provides a general theoretical framework that allows a comprehensive and in-depth understanding of the mathematical modeling of tumor growth. Next, we propose a practical mathematical model to describe the proliferation of tumor spheroids using partial differential equations, leveraging their fluorescence during the cell cycle through the Fluorescence Ubiquitination-based Cell Cycle Indicator technology. This approach differs from previous studies that relied primarily on medical imaging. Finally, this research introduces an innovative alternative for solving our complex model using recent advances in artificial intelligence. Specifically, the solutions to the proposed model were obtained using Physics-Informed Neural Networks, an approach that has produced promising results and suggests a novel perspective for this field.

In general, this work bridges the gap between traditional concepts and modern tools, paving the way for new methodologies in the mathematical modeling of cancerous tumors and offering an alternative perspective to the current state of the art.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, 378, 2019, 686--707.

[2] Ward, John P and King, John R, Mathematical modelling of avascular-tumour growth, 14, 1997, 39--69.

[3] Vittadello, Sean T and McCue, Scott W and Gunasingh, Gency and Haass, Nikolas K and Simpson, Matthew J, Mathematical models for cell migration with real-time cell cycle dynamics, 114, 2018, 1241--1253.

<footnote n="1">¹ FSR, Rabat, Morocco</footnote>

<footnote n="2">² ENSMR, Rabat, Morocco</footnote>
Variable exponent Kirchhoff-type problems involving singular and
non-local terms on Riemannian manifolds

**Communication Info**

**Authors:**

Hind Bouaam¹

Mohamed El Ouaarabi²

Said Melliani¹

¹ Applied Mathematics and
Scientific Computing
Laboratory, Faculty of Science
and Technics, Sultan Moulay
Slimane University, Beni Mellal,
BP 523, 23000, Morocco.

² Fundamental and Applied
Mathematics Laboratory,
Faculty of Sciences Aïn Chock,
Hassan II University,
Casablanca, BP 5366, 20100,
Morocco.

**Keywords:**

(1) Nonlocal terms

(2) singular term

(3) Nehari manifold method

(4) fibering maps

**Abstract**

In this paper, we investigate a bi-nonlocal elliptic
problem of the $\gamma(m)$-Kirchhoff type,
incorporating a singular term, within the framework of
complete non-compact Riemannian manifolds. Our
primary goal is to establish the existence of at least two
non-trivial weak solutions, provided that a certain
parameter remains sufficiently small.

To achieve this, we employ the Nehari manifold method
combined with the concept of fibering maps.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Bouaam, H., El Ouaarabi, M., Allalou, C., Melliani, S.: Variable exponent q(m)-Kirchhoff-type problems with nonlocal terms and logarithmic nonlinearity on compact Riemannian manifolds. Bulletin of the Malaysian Mathematical Sciences Society. \textbf{46}(3), 97 (2023).

[2] Bouaam, H., El Ouaarabi, M., Allalou, C.: Nonlocal Kirchhoff-type problem involving variable exponent and logarithmic nonlinearity on compact Riemannian manifolds. Analysis and Mathematical Physics. \textbf{13}(3), 48 (2023).

[3] Bouaam, H., El Ouaarabi, M., Allalou, C., Melliani, S.: Nonlocal $\tau(m)$-Laplacian-like problem with logarithmic nonlinearity and without Ambrosetti-Rabinowitz condition on compact Riemannian manifolds. Mathematical Methods in the Applied Sciences. \textbf{47}(7), 6097--6116 (2024).

[4] Bouaam, H., El Ouaarabi, M., Melliani, S.: Infinitely many solutions for a bi-nonlocal problem of $s(m)$-Kirchhoff-type without Ambrosetti-Rabinowitz condition. Mathematical Methods in the Applied Sciences.

[5] Bouaam, H., Ait Temghart, S., Allalou, C., Melliani, S.: Existence of Solutions to Elliptic Equations on Compact Riemannian Manifolds. Bol. Soc. Paran. Mat. .
Dynamic analysis of fractional order SEQIR epidemic model with nonlinear incidence rate and application to COVID-19 pandemic in Morocco and Italy

**Communication Info**

**Authors:**

Fatima CHERKAOUI¹

Khalid HILAL¹

Abdelaziz QAFFOU ¹

¹ Laboratory LMACS, FST of
Beni-Mellal, Sultan Moulay
Slimane University, Morocco

**Keywords:**

(1) Caputo derivative

(2) Fractional differential
equations

(3) COVID-19

**Abstract**

In December 2019, a new pandemic was detected in Wuhan, China, it is a member of the coronavirus family and has quickly spread to every nation on Earth. In this paper, we study the fractional SEQIR epidemic model with saturated incidence rate using Caputo fractional derivative describing the dynamics of COVID-19. The existence, uniqueness, positivity and boundedness of the solution are established. We show the existence of the equilibrium points (disease free and endemic equilibrium) and we investigate their local and global stability. By using MATLAB software, we provide a numerical simulation to illustrate our theoretical results and we predict the dynamics of COVID-19 in Italy and Morocco built on real-world data.

**References**

[1] R.M. Anderson and R. M.May, *Infectious diseases of humans: dynamics and control*, Oxford university press, (1991).

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

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

[4] W. Lin, *Global existence theory and chaos control of fractional differential equations*. Journal of Mathematical Analysis and Applications, 332(1)(2007), 709-726.

[5] I. Podlubny, *Fractional Differential Equations*. Academic Press, New York, (1999)
<figure><img src="image_77.png" /></figure>

# A bi-nonlocal fourth-order elliptic problem

**Communication Info**

**Authors:**

Aicha OUBAHA¹

Mohamed El OUAARABI ¹, ²

Abderrahmane RAJI¹

¹ Laboratory LMACS, Faculty of Science and Technology of Beni Mellal, Sultan Moulay Slimane University, Beni Mellal, BP 523, 23000, Morocco

² Fundamental and Applied Mathematics Laboratory, Faculty of Sciences Ain Chock, Hassan II University, Casablanca BP 5366, 20100, Morocco

**Keywords:**

(1) Fourth-order elliptic equations

(2) Kirchhoff-type problems

(3) Variational methods

**Abstract**

This paper examines a class of p(x)-Kirchhoff equations featuring bi-nonlocal terms. By applying variational methods, particularly the Mountain Pass Theorem and Ekeland's variational principle, we demonstrate the existence and multiplicity of nontrivial weak solutions for a fourth-order bi-nonlocal p(x)-Kirchhoff-type problem. This bi-nonlocal problem, involving operators with variable exponents, was first investigated by Corrêa and Augusto Cézar [2, 3].

The significance of electrorheological fluids in physical and biological phenomena has generated substantial interest in Kirchhoff-type systems. Discovered by Willis Winslow in 1949 [5], these distinctive fluids possess the remarkable ability to rapidly alter their mechanical properties when subjected to electromagnetic fields. The problem studied relates to a stationary form of the Kirchhoff equation, originally introduced by Kirchhoff in 1883 (see [4]). The idea of this article was initiated by Nguyen Thanh Chung who studied a class of fourth-order elliptic equations (see [1]).

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Chung, N.T.: Existence of solutions for perturbed fourth order elliptic equations with variable exponents. *Electronic Journal of Qualitative Theory of Differential Equations*, 2018(96), 1–19 (2018).

[2] Corrêa, F.J.S., dos Reis Costa, A.C.: A variational approach for a bi-nonlocal elliptic problem involving the p(x)-Laplacian and non-linearity with non-standard growth. *Glasgow Mathematical Journal*, 56(2), 317–333 (2013).

[3] Corrêa, F.J.S., dos Reis Costa, A.C.: On a bi-nonlocal p(x)-Kirchhoff equation via Krasnoselskii's genus. *Mathematical Methods in the Applied Sciences*, 38(1), 87–93 (2014).

[4] Kirchhoff, G.: *Mechanik*. Leipzig: Teubner, 1883.

[5] Mihailescu, M., Radulescu, V.: A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids. *Proceedings of the Royal Society A*, 462, 2625–2641 (2006).
<figure><img src="image_78.png" /></figure>

Output stabilization of infinite dimensional
bilinear systems with delayed observation

**Communication Info**

**Authors:**

Omar JARIR¹
Hassan EZZAKI¹
Khalil El KAZOUI¹

¹ LAMA Laboratory,
Department of Mathematics,
Faculty of Sciences, Ibn zohr
University, Agadir, Morocco

**Keywords:**

(1) Infinite dimensional
system

(2) delay bilinear systems

(3) output stabilization

**Abstract**

In this paper we are concerned with output stabilization of infinite dimensional bilinear systems with delayed observation. We first establish the well-posedness of such systems, and then we provide sufficient conditions for strong and weak output stabilization. Through the analysis of the wave equation and beam equation, we demonstrate the applicability and effectiveness of our proposed methods.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Lahcen Ezzaki, El Hassan Zerrik, An output stabilization of second order semilinear systems, IFAC-PapersOnLine, Volume 53, Issue 2, 2020, Pages 5889-5894.

[2] E. Zerrik, A. Akoubi, A. Ait Aadi, On the feedback stabilization of distributed bilinear systems with time delay, IFAC-PapersOnLine, Volume 55, Issue 12, 2022, Pages 729-734.

[3] Ait Aadi, A., & Hassan Zerrik, E, Strong and weak output stabilisation for distributed bilinear systems, Journal of Control and Decision, 8(3), 2020, 314–321.

[4] Zhan-Dong Mei, Bao-Zhu Guo, Stabilization for infinite-dimensional linear systems with bounded control and time delayed observation, Systems & Control Letters, Volume 134, 2019.

[5] Hamidi, Z., Ouzahra, M. & Elazzouzi, A, Strong Stabilization of Distributed Bilinear Systems with Time Delay, J Dyn Control Syst, 26, 243–254, 2020.
Mesh-Free Approaches for Solving the Advection-Dispersion Equation in
Unsaturated Flow Systems

**Communication Info**

**Authors:**

Radoine Belkanoufi¹

Ahmed Taik¹

Abdelaziz Beljadid²

¹Faculty of Sciences and
Techniques Mohammed,
Hassan II University,
Casablanca, Morocco.

²University of Ottawa, Canada.

**Keywords:**

(1) Meshless Methods

(2) Advection-Dispersion
Equation

(3) Variable Saturation

**Abstract**

In this presentation, we discuss the application of meshless techniques[1] for the numerical modeling of the Advection-Dispersion Equation (ADE) in variably saturated flow conditions [2]. We demonstrate the difficulties and challenges encountered when applying these methods to problems with varying saturation levels in porous media[3]. Through numerical simulations, we illustrate the key computational issues and limitations of the meshless approach in modeling transport phenomena under different flow conditions. The results provide important insights for environmental and hydrogeological modeling applications.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Richard, L. A. "Capillary conduction of liquids through porous mediums." physics 1.5 (1931): 318-333. [2] Authors, Title Journal, Volume, Year, Pages.

[2] van Genuchten, M. Th. "A closed-form equation for predicting the hydraulic conductivity of unsaturated soils." Soil science society of America journal 44.5 (1980): 892-898.

[3] E. J. Kansa, Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—ii solutions to parabolic, hyperbolic and elliptic partial differential equations, Computers mathematics with applications 19 (8-9) (1990) 147–161.
<figure><img src="image_79.png" /></figure>

Global stability analysis, stabilization and
synchronization of an SEIR epidemic model

**Communication Info**

**Authors:**

Farid MORTAJI1
Hassan LAARABI1
Mostafa RACHIK1
Abdelhadi ABTA2

1LAMS, Hassan II University of
Casablanca, Casablanca,
Morocco
2LAMS, Cadi Ayad University,
Safi, Morocco

**Keywords:**

SEIR epidemic model;
nonlinear dynamics; Chaos
control; backstepping control;
Lyapunov function; global
stability

**Abstract**

This paper examines an SEIR epidemic model with recruitment regulated by a constant function. The SEIR model categorizes the population into four groups (Susceptible, Exposed, Infectious, and Removed) and uses differential equations to analyze the dynamics of infectious diseases. The study determines the basic reproduction number R0 and shows that if R0<1, the disease-free equilibrium is stable, whereas if R0>1, a stable endemic equilibrium emerges. Global stability analysis is conducted using Lyapunov functions. Then, the backstepping method is applied to design a control law for eradicating the disease and synchronizing two SEIR systems. Finally, numerical simulations illustrate the theoretical findings.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Abta, A., Laarabi, H., & Talibi Alaoui, H. (2014). The Hopf bifurcation analysis and optimal control of a delayed SIR epidemic model. International Journal of Analysis, 2014, Article ID 940819. https://doi.org/10.1155/2014/940819.

[2] Agiza, H. N., & Yassen, M. T. (2001). Synchronization of Rossler and Chen dynamical systems using active control. Physics Letters A, 278, 191-197. https://doi.org/10.1016/S0375-9601(00)00777-5.

[3] Anderson, R. M., & May, R. M. (1979). Population biology of infectious diseases, part 1. Nature, 280, 361. https://doi.org/10.1038/280361a0 Anderson, R. M., & May, R. M. (1991). Infectious disease of humans: Dynamics and control. Oxford University Press.

[4] Chen, X., & Zhang, S. (2023). An SEIR model for information propagation with a hot search effect in complex networks. Mathematical Biosciences and Engineering, 20(1), 1251-1273. https://doi.org/10.3934/mbe.20
Analytical investigation of Fractal Fractional
Differential Equations with Nonlocal Conditions

**Communication Info**

**Authors:**

Najat CHEFNAJ¹

Khalid Hilal ¹

Ahmed Kajouni ¹

¹LMACS, Sultan Moulay

Slimane University, Faculty of

Sciences and Technics, Beni

Mellal, Morocco

**Keywords:**

(1) Existence theory

(2) fractal fractional derivative

(3) Existence theory

**Abstract**

Fractional calculus refers to integration or
differentiation of any order. The field has a history as
old as calculus itself, which did not attract enough
attention for a long time. In the past
decades, the theory of fractional differential equations
has become an important area of investigation because
of its wide applicability in many branches of physics,
economics and technical sciences.

This study explores the existence of solutions for a
boundary value problem involving fractal-fractional
ABC derivatives. Utilizing Darbo's and Mönch fixed-
point theorems [2] in conjunction with measures
13 of noncompactness [1], we derive our main results.
Additionally, a practical example is presented to
14 demonstrate the applicability of our theoretical
findings.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Banás J. and Goebel K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, (1980)..

[2] Granas A. and Dugundji J., Fixed Point Theory, Springer-Verlag, New York, (2003).
Asymptotics of Yule's nonsense correlation for
Ornstein-Uhlenbeck paths: The correlated case.

**Communication Info**

**Authors:**

Soukaina DOUISSI¹
Frederi Viens ²
Philip Ernst³

¹Ecole Nationale des Sciences
Appliquées, Marrakech,
Morocco

² Rice University, Houston,
Texas, United States.

³ Imperial College London,
London, United Kingdom.

**Keywords:**

(1)Malliavin Calculus

(2) Yule's Statistic

(3) Rates of Convergences

**Abstract**

In this paper we study the asymptotics of the so-
called Yule's nonsense correlation for two Orstein-
Uhlenbeck Processes (X1,X2) that are assumed to be
correlated and observed continuously over a time
interval [0,T].

Using Malliavin Calculus and other tools from the
analysis on Wiener spaces, we were able to prove that
under the hypothesis of correlation, Yule's statistic is
asymptotically Gaussian and we found the rate of this
convergence in law which is of the order of 1/T¹/² for
the Wasserstein's metric.

Several applications to statistical inference problems
are proposed including in particular a test of hypothesis
that is proved to be asymptotically powerful.

This paper extends the line of research of references [1],
[2], [3] and [4].

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] Ernst, P.A., Rogers, L.C.G., and Zhou, Q.* (2025) Yule's "nonsense correlation": moments and density. *Bernoulli*, 31(1): 412-431.

[2] Ersnt, P., Huang, D., Viens, F. Yule's nonsense correlation for Gaussian random walks, SPA, 162, 423-455,2023.

[3] Douissi, S., Es-Sebaiy, K., Viens, F. Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths, a Wiener chaos Approach, Electro.J. Statist 16(1), 3176-3211,2022.

[4] Esrnt, P., Shepp, L., Wyner, A. Yule's nonsense correlation solved. The Annals of Statistics, 45 (4), 1789-1809 (2017).
Existence and uniqueness of solutions for a p(x)-Schrödinger-type equation
under Fourier boundary conditions

**Communication Info**

**Authors:**

Hayat BENKHALOU¹

Ayman EL JANATHI²

¹Abdelmalek Essaâdi

University, Tétouan, Morocco

²Abdelmalek Essaâdi

University, Tétouan, Morocco

**Keywords:**

(1) Existence and uniqueness

(2) Sobolev spaces with variable exponent

(3) Fourier boundary conditions

(4) Renormalized solutions

**Abstract**

In this paper we prove the existence and uniqueness of renormalized solutions to the nonlinear elliptic problem defined as follows

$$ egin{cases} 
-\mathrm{div}(a(x, |\nabla u|)\nabla u) + |u|^{p(x)-2}u = f(x) - \mathrm{div}(\varphi(x, u)) & \text{in} \\ 
ku + (a(x, |\nabla u|)\nabla u - \varphi(x, u))\eta = g & \text{in } \partial\Omega 
\end{cases} 
$$

in the setting of Sobolev spaces with variable exponents, where $\Omega$ is a bounded open subset in $\mathbb{R}^N$ ($N \ge 3$) with Lipschitz boundary. $\eta$ is the outer unit normal vector on $\partial\Omega$ and $k$ is a strictly positive real constant. The nonlinear term $\varphi(x, u)$ verifies some growth condition, the right hand-side $f$ belongs to $L^1(\Omega)$ and $g \in L^1(\partial\Omega)$.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] E. Azroul, M. B. Benboubker and S. Ouaro, Entropy solutions for nonhomogeneous Neumann Problems involving the generalized p(x)-Laplace Operator, J. Appl. Anal. Comput., 3 (2) 2013, 105-121.

[2] M.B. Benboubker, H. Benkhalou, H. Hjiaj, I. Nyanquini, Entropy solutions for elliptic Schrödinger type equations under Fourier boundary conditions. Rend. Circ. Mat. Palermo, II. Ser 72, 2023, 2831-2855.

[3] M. Ben Cheikh Ali and O. Guibé, Nonlinear and non-coercive elliptic problems with integrable data. Adv. Math. Sci. Appl., 16(1), 2006, 275-297.

[4] M. Ben Cheikh Ali and O. Guibé, Nonlinear and non-coercive elliptic problems with integrable data. Adv. Math. Sci. Appl., 16(1), 2006, 275-297.

[5] M. F. Betta, O. Guibé, and A. Mercaldo, Uniqueness for Neumann problems for nonlinear elliptic equations. Communications on Pure and Applied Analysis, 259(3), 2017, 898-924.
A coupled continuous dynamical system for
nonconvex optimization.

**Communication Info**

**Authors:**

Aïcha BALHAG ¹
Abderrahim JOURANI ²

¹ Laboratoire de Mathématique, Modélisation et Systèmes Automatiques
Ecole Normale Supérieure de Marrakech
Université Cadi Ayyad.

² Institut de Mathématiques de
Bourgogne .UMR 5584 CNRS
Université Bourgogne
F-21000 Dijon, France

**Keywords:**

(1) Kurdyka-Łojasiewicz
property.

(2) Non convex minimization
problem.

(3) Desingularization function.

**Abstract**

In this paper, we deal with a coupled continuous dynamical
system associated with an unconstrained (not necessarily
convex) minimization problem. Assuming that a regularization
of the objective function satisfies the Kurdyka-Łojasiewicz
property, we show that the trajectory converges towards a
critical point of the objective function. We also study the
convergence rate in a manner dependent on a one-dimensional
worst-case gradient system as used by Bégout-Bolte-Jendoubi
in [1] for quasi-gradient systems, it yields convergence results
related to the geometry of the objective function via the
desingularization function. This study is a generalization of
many previous results. Moreover, when the function is twice
differentiable, our system is equivalent to a second-order in
time differential equation combining hessian-driven damping
with time rescaling parameters. Our results exhibit novelty by
offering study of asymptotic convergence in general case of
these parameters in non-convex function. it paves the way for
the investigation of a new family of inertial algorithms for non-
convex optimization with a good asymptotic convergence
properties.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] P. Begout, J. Bolte, M. Jendoubi, On damped second-order gradient systems, J. Differ. Equ., 259 (7-8)

[2] Alvarez, F., Attouch, H., Bolte, J., Redont, P.: A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics. J. Math. Pures Appl. (9)

[3] Boł, R. I., Csetnek, E. R., László, S. C. (2020). A second-order dynamical approach with variable damping to nonconvex smooth minimization. Applicable Analysis, 99(3), 361-378.
# Segmentation of Transition Matrices Using Eigenvalues

## Communication Info

**Authors:**

Chaimaa RIAHI<fnref n="1" />

Youssef EL FOUTAEYNI <fnref n="2" />

**Keywords:**

(1) Profit maximization

(2) Markov chain

(3) Eigenvalues

(4) Matrix Decomposition

## Abstract

Understanding state dynamics in Markov processes is essential for many real-world applications. In this work, we introduce a spectral-based approach to segment transition matrices, revealing hidden structures in stochastic systems. By leveraging eigenvalues [4] and eigenvectors, we identify meaningful segments that maintain key transition properties while uncovering hidden patterns. Our method extends the Markov chain-based temperature estimation model by **Riahi et al.** [1], incorporating spectral properties [5] to enhance segmentation techniques. Additionally, our approach aligns with bioeconomic equilibrium modeling principles discussed in **Riahi et al.** [2], reinforcing its relevance to complex dynamic systems. This framework is particularly useful for applications in climate modeling [3], financial time series analysis, and other dynamic systems. We discuss theoretical justifications, computational feasibility, and initial experimental results, which confirm the effectiveness of spectral segmentation in uncovering hidden structures within Markov chains.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Riahi, C., Agmour, I., & El Foutayeni, Y. (2023). Impact of temperature on profit estimation of two fishermen exploiting three competing species using Markov chain. Advanced Mathematical Models & Applications, 8(1), 65-82.

[2] Riahi, C., El Foutayeni, Y., Guerbaz, R. (2019). Modélisation bioéconomique des équilibres Multi-espèces avec interactions éco-systémiques et de marché. ICRAMCS, 144. [https://icramcs2019.sciencesconf.org]

[3] Riahi, C., Agmour, I., El Foutayeni, Y., Achtaich, N. (2024). Impact of wind speed on profit maximization in dual-fishermen exploitation of tritrophic prey-predator fish populations. Communications in Mathematical Biology and Neuroscience, 2024 (2024), Article ID 7.

[4] Delbianco, F., Fioriti, A. & Tohmé, F. Markov chains, eigenvalues and the stability of economic growth processes. Empir Econ 64, 1347-1373 (2023). https://doi.org/10.1007/s00181-022-02276-8

[5] Seabrook, E., & Wiskott, L. (2023). A Tutorial on the Spectral Theory of Markov Chains. In Neural Computation (Vol. 35, Issue 11, pp. 1713-1796). MIT Press. https://doi.org/10.1162/neco_a_01611

<footnote n="1">¹ University Hassan 2,
Casablanca, Morocco</footnote>

<footnote n="2">² University Cadi Ayyad,
Marrakech, Morocco</footnote>
<figure><img src="image_80.png" /></figure>

# Mathematical Modeling of Ecosystem Interactions

**Communication Info**

**Authors:**

Fatima-Ezzahra AZZOUGAGH¹
Imane AGMOUR¹
Youssef EL FOUTAYENI²

¹Cadi Ayyad University,
Marrakech, Morocco

³University of Hassan II,
Casablanca, Morocco

**Keywords:**

(1) Mathematical Modeling

(2) Ecosystem Interactions

(3) Climate Change

**Abstract**

The study of bioeconomic models is a crucial tool for understanding the complex relationship between natural resources and their economic exploitation, as well as the impact of human activities on the environment, in order to determine a sustainable management strategy.

In this context, we can cite [1, 2] which provides us a bioeconomic modeling of the exploitation of marine species, in addition to [3, 4], where the authors showed the influence of pollution on marine ecosystems. We also mention the effect of the wind which is the subject of the article [5]. In this presentation, we seek to synthesize current research and paves the way for future researches aimed at integrating the stochastic study into future work.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

**References**

[1] P. F. Verhulst, Notice sur la loi que suit la population dans son accroissement, Corresp. Math. Phys., 10 (1838):113-121.

[2] Y. El foutayeni, M. Khaladi and A. Zegzouti, A generalized Nash equilibrium for a bioeconomic problem of fishing, Stud. Inform. Univ., 10(2012), 186-204.

[3] I. Agmour, N. Baba, S. Rhila, N. Achtaich, Y. El foutayeni, M. Rachik, Optimal Control Of Pollution Rate In A Spatiotemporal Bioeconomic Model. Applied Mathematics E - Notes. 24(2024), 4-18.

[4] F. Bendahou, N. Baba, Y. El foutayeni, N. Achtaich, Impact of pollution on sardine, sardinella, and mackerel fishery: a bioeconomic approach, Commun. Math. Biol. Neurosci., 2023(2023).

[5] C. RIAHI, I. Agmour, Y. El foutayeni, N. Achtaich, Impact of wind speed on profit maximization in dual-fishermen exploitation of tritrophic prey-predator fish populations, Commun. Math. Biol. Neurosci., 2024(2024).
<figure><img src="image_81.png" /></figure>

# Numerical Simulation of the Spatial Solow Model

## Communication Info

**Authors:**

Abdellah EL AABBADI<fnref n="1" />

Hicham EL BOUJAOUI<fnref n="1" />

Abderrazak BOUFALA<fnref n="2" />

**Keywords:**

(1) Spatial economics

(2) Deep learning

(3) Solow Growth Model

(4) Partial Differential

Equations (PDEs)

## Abstract

This research presents a spatial-temporal [1] extension of the Solow growth model [3], operating in continuous time and space domains. We establish formal mathematical proof regarding the existence of a solution to this spatially-distributed economic growth framework and demonstrate its asymptotic convergence properties toward a stationary equilibrium. The concluding section of the manuscript offers numerical simulations across diverse parameterizations, providing empirical validation of the theoretical convergence results and illustrating the spatial-dynamic properties of the model under various initial conditions.

© ICRAMCS 2025 Proceedings ISSN: 2605-7700

## References

[1] Camacho, Carmen, and Benteg Zou.. The spatial Solow model. *Economics Bulletin* 18: 1-11 (2004)

[2] I.E. Lagaris, A. Likas, D.I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations, *IEEE Trans. Neural Netw.* 9 987-1000. (1998)

[3] Solow Robert. "A Contribution to the Theory of Economic Growth," *Quarterly Journal of Economics* 70: 65-94. (1956)

<footnote n="1">¹ ENSA UIZ, Agadir, Morocco</footnote>

<footnote n="2">² College of Law and Economics</footnote>

<footnote>UIZ, Agadir, Morocco</footnote>