Email: [email protected] Abstract: In this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equat...

This paper successfully applies the Adomian decomposition  and the modified Laplace Adomian decomposition methods to find  the approximate solution of a nonlinear fractional Volterra-Fredholm integro-differential equation. The reliability of the methods and reduction in the size of the computational work give these methods a wider applicability. Also, the behavior of the solution can be formall...

This paper is concerned with obtaining the approximate solution of Fredholm-Volterra integro-differential equations. Properties of the Shannon wavelets and connection coefficients are first presented. We design a numerical scheme for these equations using the Galerkin method incorporated with the Shannon wavelets approximation and the connection coefficients. We will show that using this techni...

In this paper, we investigate the numerical study of nonlinear Fredholm integro-differential equation with fractional Caputo-Fabrizio derivative. We use Hermite wavelets and collocation technique to approximate exact solution by reducing a algebraic system. Furthermore, apply method on certain examples check its accuracy validity.

A fractional calculus concept is considered in the framework of a Volterra type integro-differential equation, which employed for self-consistent description high-gain free-electron laser (FEL). It shown that Fox H-function Laplace image kernel also known as FEL equation with Caputo–Fabrizio derivative. Asymptotic solutions are analyzed well.

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

Fractional calculus, which deals with the concept of fractional derivatives and integrals, has become an important area research, due to its ability capture memory effects non-local behavior in modeling real-world phenomena. In this work, we study a new class Volterra–Fredholm integro-differential equations, involving Caputo–Katugampola derivative. By applying Krasnoselskii Banach fixed-point t...

In this article, the numerical solution of mixed Volterra–Fredholm integro-differential equations multi-fractional order less than or equal to one in Caputo sense (V-FIFDEs) under initial conditions is presented with powerful algorithms. The method based upon quadrature rule aid finite difference approximation derivative usage collocation points. For treatments, our technique converts V-FIFDEs ...