Existence of mild solutions for $\xi$-Caputo fractional integro-differential evolution problems.

Abstract

The aim of this paper is to investigate the existence of mild solutions to a nonlocal $\xi$-Caputo fractional semilinear integro-differential evolution equation in any arbitrary Banach space. The existence of the results is proved by using the fixed point theorem for condensing maps. To illustrate our theoretical results, a non-trivial example is given as an application.