Abstract The Cauchy problem of a time-space fractional partial differential equation which has as particular cases the Klein-Gordon equation, generalized expression heat and two apparently unexplored integro-differential equations in context physics, is proposed solved for delta initial condition. Series H-Fox functions are obtained solution.

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

The main purpose of this paper was to efficiently apply the new procedure solve Linear Systems Volterra Integro-Fractional Differential Equations (LSVIFDEs) in Caputo sense for fractional order by means Fourth Block-by-Block approach with forward finite difference approximation. With technique, authors use an appropriate process convert our problem into analogous piecewise iterative algebraic l...

Abstract The shifted Chebyshev polynomials of the fifth kind (SCPFK) and collocation method are employed to achieve approximate solutions a category functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for numerical solution problem under study. suggested changes s...

In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Abstract The aim of this article is to discuss the uniqueness and Ulam–Hyers stability solutions for a nonlinear fractional integro-differential equation involving generalized Caputo operator. used operator generated by iterating local integral form $(I_{a}^{\rho }f)(t)=\int _{a}^{t}f(s)s^{\rho -1}\,ds$ ( <...