Nonlocal Conformable-Fractional Differential Equations with a Measure of Noncompactness in Banach Spaces

This paper deals with the existence of mild solutions for the following Cauchy problem: , where is the so-called conformable fractional derivative. The linear part A is the infinitesimal generator of a uniformly continuous semigroup on a Banach space X, f and are given functions. The main result is proved by using the Darbo–Sadovskii fixed point theorem without assuming the compactness of the family and the Lipshitz condition on the nonlocal part