Existence of mild solutions for fractional non-instantaneous impulsive integro-differential equations with nonlocal conditions

Abstract

This paper is concerned with the existence of mild solutions for a class of fractional semilinear integro-differential equations having non-instantaneous impulses. The result is obtained by using noncompact semigroup theory and fixed point theorem. The obtained result is illustrated by an example at the end.

Existence results of noninstantaneous impulsive fractional integro-differential equation

“…Existence of mild solution of noninstantaneous impulsive fractional differential equation with local initial condition has been studied by Li and Xu [33]. Meraj and Pandey [34] studied the existence of mild solutions of nonlocal semilinear evolution equation using Krasnoselskii's fixed point theorem. In this article, we study the existence of mild solutions of…”

Approximate controllability of multi-term time-fractional stochastic differential inclusions with nonlocal conditions

“…There are several definitions of fractional derivatives such as Hadamard derivative, Grunwald Letnikov derivative, Riemann Liouville fractional derivative, Caputo fractional derivative etc. For the basics of fractional calculus, one can refer to the monographs [10,15,21,22] and for recent developments in this field, we can make references to the papers [2,6,11,20,32] and references cited therein.…”