a class of global fractional order projective dynamical systems involving set valued perturbations this paper studies a class of global fractional order projective dynamical systems involving set valued perturbations in real separable hilbert spaces we prove that the set of solutions for this type of systems is nonempty and closed under some suitable conditions furthermore we show that the set of solutions is continuous with respect to initial value in the sense of hausdorff metric finally an interesting numerical example is given to illustrate the validity of the main theorem presented in this paper

brief note on the variation of constants formula for fuzzy differential equations this note gives a theory of state transition matrices for linear systems of fuzzy differential equations this is used to give a fuzzy version of the classical variation of constants formula a simple example of a time independent control system is used to illustrate the methods while similar problems to the crisp case arise for time dependent systems in time independent cases the calculations are elementary solutions of eigenvalue eigenvector problems in particular for nonnegative or nonpositive matrices the problems at each level set can easily be solved in matlab to give the level sets of the fuzzy solution

two point boundary value problems of undamped uncertain dynamical systems in this paper we study two point boundary value problems of a class of uncertain dynamical systems i e undamped uncertain dynamical systems we introduce the concept of large solutions and small solutions for two point boundary value problems of undamped uncertain dynamical systems and under some conditions establish the existence and uniqueness of large solutions and small solutions and settle the relationship between large solutions and small solutions

tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose the oil palm frond a lignocellulosic material is a high yielding energy crop that can be utilized as a promising source of xylose it holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection storage and cropping practices the aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the oil palm frond through a fuzzy fractional kinetic model the approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized laguerre polynomials the results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model a new fractional kinetic equation under uncertainty was addressed to depict the chemical reaction arising in palm oil frond an efficient numerical simulation based on a tau method was derived to solve the proposed kinetic equation different cases were solved to demonstrate the validity and efficiency of the proposed technique

fuzzy fractional functional integral and differential equations this paper is devoted to considering the existence and uniqueness results for fuzzy fractional functional integral equations employing the contraction principle moreover the approach is followed to prove the existence and uniqueness of solutions for the fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives finally the solution to fuzzy fractional functional initial value problem under caputo type fuzzy fractional derivatives by a modified fractional euler method mfem is presented the method is illustrated by solving some examples

nontrivial periodic solutions for delay differential systems via morse theory abstract the existence of the nontrivial periodic solutions to the system of delay differential equations 1 1 x t f x t is investigated where x r n f c r n r n we prove several new existence results via morse theory and the galerkin methods

a system of fractional order interval projection neural networks in this paper a system of fractional order interval projection neural networks is introduced and investigated under some suitable assumptions the existence and uniqueness of the equilibrium point of this type of interval projection neural networks is proved moreover exponential stability of this type of neural networks is obtained also in the last section we give two numerical examples to demonstrate the validity of our results

differentials of fuzzy functions abstract in this paper the radstrom embedding theorem proc amer math soc 3 1952 165 is generalized and is used to define the concept of the differential of a fuzzy function

on a system of fuzzy fractional differential inclusions with projection operators abstract the aim of this paper is to introduce and study a class of fuzzy fractional differential inclusions with projection operators which captures the desired features of both fuzzy differential inclusions and fractional order projective dynamical systems within the same framework the existence of solutions for the open situation is proved by using continuous selection theorem moreover the existence of solutions for the closed situation is showed by employing lipschitzean selection theorem and fixed point theorem respectively furthermore an application and a numerical example are also given

stability and periodicity in fuzzy differential equations formulations of fuzzy differential equations des in terms of the hukuhara derivative do not reproduce the rich and varied behavior of crisp des another interpretation in terms of differential inclusions expressed level setwise overcomes much of this deficiency and opens up for profitable investigation such properties as stability attraction periodicity and the like this is especially important for investigating continuous systems which are uncertain or incompletely specified this paper studies studies lyapunov stability of fuzzy des and the periodicity of the fuzzy solution set for both the time dependent and autonomous cases

instabilities in threshold diffusion equations with delay the introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio temporal chaos in this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria periodic orbits and travelling waves importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback direct numerical simulations are used to confirm our bifurcation analysis and to probe some of the rich behaviour possible for mixed feedback

multiplicity results for periodic solutions to delay differential equations via critical point theory abstract by the critical point theory we study the existence and multiplicity of periodic solutions to the following system of delay differential equations x t f x t r where x r n f c r n r n and r 0 is a given constant a sufficient condition on the existence and multiplicity of periodic solutions for eq is obtained to the authors knowledge this is the first time the existence of periodic solutions to systems of delay differential equations is dealt with by using variational approaches directly

the multiplier equation and its application to s solutions of a differential delay equation stability and uniqueness of slowly oscillating periodic solutions are two important questions concerning differential delay equations it is suggested in 6 that these two problems are closely related to each other although many results on the existence of such solutions have been established see 7 and refs therein results on their uniqueness and stability are comparatively few even in the simplest cases a slowly oscillating periodic or sop solution of

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

the solvability of fuzzy fractional partial differential equations under caputo gh differentiability the foundation of the concepts of fuzzy fractional integral and caputo gh partial for fuzzy valued multivariable functions is defined as a result fuzzy fractional partial differential equations are considered and the appropriateness of local boundary value problems for hyperbolic equations is proved we present two new results on the existence of two kinds of gh weak solutions of these problems the first result is based on the banach fixed point theorem with the lipschitz condition of functions on the right hand side of equations the second result is based on the nonlinear alternative of the schauder type for fuzzy valued continuous functions without the lipschitz condition moreover we indicate the boundedness and continuous dependence of solutions on the initial data of the problems our models are embedded in the sense of caputo gh differentiability some examples are presented to illustrate the results

characteristic multipliers and stability of symmetric periodic solutions of x t g x t 1 on etudie l equation differentielle scalaire a retard x t g x t 1 a retroaction negative on suppose que la fonction non lineaire g est impaire et monotone on demontre que des solutions periodiques x t de type legerement oscillant satisfaisant la condition de symetrie x t x t 2 t r sont non degenerees et ont toutes des multiplicateurs de floquet non triviaux dans le cercle unite

day to day dynamic network disequilibria and idealized traveler information systems in this paper we present tatonnement models for calculating static wardropian user equilibria on congested networks with fully general demand and cost structures we present both a qualitative analysis of stability and numerical studies which show that such an approach provides a reliable means for determining static user equilibria we also describe circumstances for which these models depict day to day adjustments from one realizable disequilibrium state to another and how these adjustment processes differ depending on the quality of the information being provided by abstract traveler information systems specifically we demonstrate that such dynamic adjustment processes settle down to equilibria both when information is complete and when it is incomplete

random fuzzy fractional integral equations theoretical foundations abstract this paper presents mathematical foundations for studies of random fuzzy fractional integral equations which involve a fuzzy integral of fractional order we consider two different kinds of such equations their solutions have different geometrical properties the equations of the first kind possess solutions with trajectories of nondecreasing diameter of their consecutive values on the other hand the solutions to equations of the second kind have trajectories with nonincreasing diameter of their consecutive values firstly the existence and uniqueness of solutions is investigated this is showed by using a method of successive approximations an estimation of error of n th approximation is given also a boundedness of the solution is indicated to show well posedness of the considered theory we prove that solutions depend continuously on the data of the equations some concrete examples of random fuzzy fractional integral equations are solved explicitly

reflection groups on the octave hyperbolic plane for two different integral formskof the exceptional jordan algebra we show that aut kis generated by octave reflections these provide geometric examples of discrete reflection groups acting with finite covolume on the octave or cayley hyperbolic plane oh2 the exceptional rank one symmetric space the isometry group of the plane is the exceptional lie groupf4 20 our groups are defined in terms of coxeter s discrete subring k of the nonassociative division algebra o and we interpret them as the symmetry groups of lorentzian lattices over k we also show that the reflection group of the hyperbolic cell over k is the rotation subgroup of a particularrealreflection group acting onh8 oh1 part of our approach is the treatment of the jordan algebra of matrices that are hermitian with respect to any real symmetric matrix

differential inclusions for fuzzy maps we introduce the problems of differential inclusions for fuzzy maps and study the existence of solutions to these problems by the continuous selection theorem and fixed point theorems respectively

stability of nonlinear waves in a ring of neurons with delays abstract in this paper we consider a ring of identical neurons with self feedback and delays based on the normal form approach and the center manifold theory we derive some formula to determine the direction of hopf bifurcation and stability of the hopf bifurcated synchronous periodic orbits phase locked oscillatory waves standing waves mirror reflecting waves and so on in addition under general conditions such a network has a slowly oscillatory synchronous periodic solution which is completely characterized by a scalar delay differential equation despite the fact that the slowly oscillatory synchronous periodic solution of the scalar equation is stable we show that the corresponding synchronized periodic solution is unstable if the number of the neurons is large or arbitrary even