Existence and Uniqueness of Mild Solutions for Fractional Integrodifferential Equations

Abstract

The aim of this paper is to prove the existence and uniqueness of mild solution of a class of l nonlinear fractional integrodifferential equations {█((d^q u(t))/(dt^q )+Au(t)=∫_0^t▒f(t,s,x(s) )ds+∫_0^t▒〖a(t-s)g(s,y(s) )ds, t∈[0,T],〗@u(0)=u_(o.) )┤ in a Banach space X, where 0<q<1. Results are obtained by fixed point theorem. The results are established by using Krasnoselskii’s fixed point theorem and the contraction mapping principle.