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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 540351, 9 pages
http://dx.doi.org/10.1155/2014/540351
Research Article

Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

1Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, China
2Department of Information Engineering, Guangdong Medical College, Dongguan, Guangdong 523808, China

Received 8 May 2014; Revised 29 June 2014; Accepted 1 July 2014; Published 15 July 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2014 Wenzhe Xie 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

By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al-Refai (2012). As applications, an example is presented to illustrate our main results.