Abstract Cauchy problem for fractional functional differential equations

Abstract

In this paper, the existence and continuation of solutions for the Cauchy initial value problem of fractional functional differential equations in an arbitrary Banach space is discussed under hypotheses based on Carathéodory condition and the measure of noncompactness. In addition, an example is given to show that the criteria on existence of solutions for the initial value problem of fractional differential equations in finite-dimensional spaces may not be true in infinite-dimensional cases.