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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 493164, 8 pages
Research Article

Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China

Received 27 April 2013; Accepted 7 August 2013

Academic Editor: Yong Zhou

Copyright © 2013 Chaozhu Hu 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.


By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.