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.