Existence of Stepanov-like weighted pseudo almost automorphic solutions of fractional integro-differential equations via measure theory

Abstract

In this paper, we discuss $\mu$- Stepanov-like  pseudo almost automorphic solutions of fractional integro differential equations. First we explore the important properties of $\mu$- Stepanov-like pseudo almost automorphic functions including composition principle. Composition principle is very useful property when we apply the theory to differential equations. We prove the result with and without Lipschitz condition on the forcing term. At the end an example is given to illustrate our analytical findings.