Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...

We study S-asymptotically ω-periodic mild solutions of the semilinear Volterra equation u′(t) = (a ∗ Au)(t) + f(t, u(t)), considered in a Banach space X, where A is the generator of an (exponentially) stable resolvent family. In particular, we extend recent results for semilinear fractional integro-differential equations considered in [4] and for semilinear Cauchy problems of first order given ...

this paper presents a computational method for solving two types of integro-differential equations, system of nonlinear high order volterra-fredholm integro-differential equation(vfides) and nonlinear fractional order integro-differential equations. our tools for this aims is operational matrices of integration and fractional integration. by this method the given problems reduce to solve a syst...

In this paper, we study the existence of weighted pseudo almost automorphic mild solutions of integro-differential equations with fractional order 1 < α < 2, here A is a linear densely defined operator of sectorial type on a complex Banach space X. This paper also deals with existence of weighted pseudo almost automorphic mild solutions of semilinear integro-differential eqautions with A is the...

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demo...