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Abstract and Applied Analysis
Volume 2012, Article ID 615230, 14 pages
Research Article

Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations

1School of Mathematical Sciences, University of Jinan, Shandong, Jinan 250022, China
2Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
3School of Control Science and Engineering, University of Jinan, Shandong, Jinan 250022, China

Received 8 May 2012; Revised 12 June 2012; Accepted 13 June 2012

Academic Editor: Dumitru Baleanu

Copyright © 2012 Qiuping 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.


We discuss the initial value problem for the nonlinear fractional differential equation , where , , and , , is the standard Riemann-Liouville fractional derivative and is a given continuous function. We extend the basic theory of differential equation, the method of upper and lower solutions, and monotone iterative technique to the initial value problem. Some existence and uniqueness results are established.