Pseudo almost automorphic behavior of solutions to a semi-linear fractional differential equation

Abstract

In this paper, we shall deal with $\mu$-pseudo almost automorphic solutions to a semi-linear fractional differential equation by new concept of $\mu$-pseudo almost automorphic functions presented recently. We first establish some new properties of $\mu$-pseudo almost automorphic functions, and then we apply the results obtained to prove some existence theorems combined with the Leray-Schauder alternative theorem.