Journal of Applied Mathematics
Volume 2012 (2012), Article ID 901942, 18 pages
http://dx.doi.org/10.1155/2012/901942
Research Article

A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations

Fang Li,1 Jin Liang,2 Tzon-Tzer Lu,3 and Huan Zhu4

1School of Mathematics, Yunnan Normal University, Kunming 650092, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
4Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

Received 12 February 2012; Accepted 3 March 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Fang Li et al. 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

This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. As an application, the existence of the mild solution to a nonlocal Cauchy problem for a concrete integrodifferential equation is obtained.