Properties on measure pseudo almost automorphic functions and applications to fractional differential equations in Banach spaces

Abstract

In this article, we establish some new composition theorems on measure pseudo almost automorphic functions via measure theory. The obtained compositions theorems generalize those established under the well-known Lipschitz conditions or the classical uniformly continuous conditions. Then using the theories of resolvent operators and fixed point theorem, we investigate the existence and uniqueness of measure pseudo almost automorphic solutions to a fractional differential equation in Banach spaces.

Keywords

• Composition theorems
• measure pseudo almost automorphic function
• fractional differential equation