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Abstract and Applied Analysis
Volume 2014, Article ID 758390, 11 pages
http://dx.doi.org/10.1155/2014/758390
Research Article

Existence and Uniqueness of the Solutions for Fractional Differential Equations with Nonlinear Boundary Conditions

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 3 March 2014; Accepted 29 May 2014; Published 19 June 2014

Academic Editor: Abdelghani Bellouquid

Copyright © 2014 Xiping Liu 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

We study the existence and uniqueness of the solutions for the boundary value problem of fractional differential equations with nonlinear boundary conditions. By using the upper and lower solutions method in reverse order and monotone iterative techniques, we obtain the sufficient conditions of both the existence of the maximal and minimal solutions between an upper solution and a lower solution and the uniqueness of the solutions for the boundary value problem and present the iterative sequence for calculating the approximate analytical solutions of the boundary value problem and the error estimate. An example is also given to illustrate the main results.