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

Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations

Chunhai Kou1 , Jian Liu1 and Yan Ye3

1Department of Applied Mathematics, Donghua University, Shanghai 201620, China
3College of Information Sciences and Technology, Donghua University, Shanghai 201620, China

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.