In this paper, we establish the new forms of Riemann-type fractional integral and derivative operators. The novel operator is proved to be bounded in Lebesgue space some classical differential operators are obtained as special cases. properties like semi-group, inverse certain others discussed its weighted Laplace transform evaluated. Fractional integro-differential free-electron laser (FEL) ki...

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.

We study a dynamic model for viscoelastic materials based on a constitutive equation of fractional order. This results in an integrodifferential equation with a weakly singular convolution kernel. We discretize in the spatial variable by a standard Galerkin finite element method. We prove stability and regularity estimates which show how the convolution term introduces dissipation into the equa...

Abstract This article discusses the stability results for solution of a fractional q -integro-differential problem via integral conditions. Utilizing Krasnoselskii’s, Banach fixed point theorems, we demonstrate existence and uniqueness results. Based on obtained, conditions are provided to ensure generalized Ulam Ulam–Hyers–Rassias stabilities original system. The illustrated by two examples.

* Correspondence: [email protected] Department of Mathematics and Computer Sciences, Cankaya University, Eskisehir Yolu 29. km, YukariYurtcu Mah. No 80, 06810 Yenimahalle, Ankara, Turkey Full list of author information is available at the end of the article Abstract Our aim in this work is to study the existence and the attractivity of solutions for a system of delay partial integro-differ...

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 $(I_{a}^{\rho }f)(t)=\int _{a}^{t}f(s)s^{\rho -1}\,ds$ ( <...