Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces

Abstract

This paper is devoted to study the existence of solutions of a Cauchy type problem for a nonlinear fractional differential equation, via the techniques of measure of noncompactness. The investigation is based on a new fixed point result which is a generalization of the well known Darbo's fixed point theorem. The main result is less restrictive than those given in the literature. Some illustrative examples are given. © 2013 Versita Warsaw and Springer-Verlag Wien.