Advances in Difference Equations
Volume 2010 (2010), Article ID 158789, 10 pages
doi:10.1155/2010/158789
Research Article

Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations

Fang Li1 and Gaston M. N'Guérékata2

1School of Mathematics, Yunnan Normal University, Kunming 650092, China
2Department of Mathematics, Morgan State University, 1700 East Cold Spring Lane, Baltimore, MD 21251, USA

Received 1 April 2010; Accepted 17 June 2010

Academic Editor: Tocka Diagana

Copyright © 2010 Fang Li and Gaston M. N'Guérékata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.