Existence of mild solutions for non-instantaneous impulsive ξ-Caputo fractional integro-differential equations

Abstract

The aim of this paper is to investigate the existence of mild solutions for a nonlocal ξ-Caputo fractional non-instantaneous impulses semilinear integro-differential equation in a Banach space. The proofs are based on some fixed point theorems for condensing maps. As an application, an example is given to illustrate our theoretical results.