Pseudo Almost Automorphic Mild Solutions for Two-Term Fractional Order Differential Equations via Measure Theory

In this article, by measure theory, we introduce and study the concept of µ-Stepanov like functions.We present new result on composition theorem for the space of such functions.As applications, we establish some sufficient criteria for the existence and uniqueness of pseudo almost automorphic mild solutions to two-term fractional differential equations, under the assumption that the forcing terms of the equation are µ-Stepanov like pseudo almost automorphic function.The working tools are an operator theoretical approach based on certain families of strongly continuous operators Definition 2.1, Banach fixed point theorem and Leray-Shauder alternative theorem.An example is given for illustration.