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

Abstract EN

This paper deals with the existence of mild solutions for the following Cauchy problem: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ, where dα./dtα is the so-called conformable fractional derivative.

The linear part A is the infinitesimal generator of a uniformly continuous semigroup Ttt≥0 on a Banach space X, f and g are given functions.

The main result is proved by using the Darbo–Sadovskii fixed point theorem without assuming the compactness of the family Ttt>0 and the Lipshitz condition on the nonlocal part g.