Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations

Abstract

We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations dqu(t)/dtq+Au(t)=f(t,u(t))+∫0ta(t−s)g(s,u(s))ds, t∈[0,T], u(0)=u0, in a Banach space X, where 0<q<1. New results are obtained by fixed point theorem. An application of the abstract results is also given.