Existence of mild solution for fractional nonlocal neutral impulsive integro-differential equations with state-dependent delay

Abstract

In this paper, we consider a class of impulsive nonlocal fractional neutral integrodifferential equation with state-dependent delay in Banach spaces. First we prove the existence and uniqueness of mild solution by using the fixed point theorem of nonlinear alternative of Frigon-Granas type for contractions maps in Frechet space combined with α-resolvent family. Finally an example is provided to illustrate the obtained the results.