Advances in Difference Equations
Volume 2010 (2010), Article ID 340349, 10 pages
doi:10.1155/2010/340349
Research Article

Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces

Zhi-Wei Lv,1 Jin Liang,2 and Ti-Jun Xiao3

1Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
3Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, China

Received 4 January 2010; Accepted 8 February 2010

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2010 Zhi-Wei Lv 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

A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.