Existence results for Riemann–Liouville fractional evolution inclusions in Banach spaces

Abstract

The aim of this work is to study the existence of mild solution for semi-linear fractional evolution inclusions involving Riemann–Liouville derivative in Banach space. We prove our main result by introducing a regular measure of noncompactness in weighted space of continuous functions and using the condensing multivalued maps theory. Our result improve and complement several earlier related works. An example is given to illustrate the applications of the abstract result.