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.