Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 142175, 15 pages
doi:10.1155/2010/142175
Research Article

Existence and Uniqueness of Solutions for the Cauchy-Type Problems of Fractional Differential Equations

Chunhai Kou,1 Jian Liu,1 and Yan Ye2

1Department of Applied Mathematics, Donghua University, Shanghai 201620, China
2College of Information Sciences and Technology, Donghua University, Shanghai 201620, China

Received 30 October 2009; Revised 21 January 2010; Accepted 25 January 2010

Academic Editor: Guang Zhang

Copyright © 2010 Chunhai Kou 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

By using the Banach fixed point theorem and step method, we study the existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations. Meanwhile, by citing some counterexamples, it is pointed out that there exist a few defects in the proofs of the known results.