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Abstract and Applied Analysis
Volume 2013, Article ID 847184, 7 pages
Research Article

Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems

1Department of Mathematics, Neka Branch, Islamic Azad University, P.O. Box 48411-86114, Neka, Iran
2Department of Mathematics, Sari Branch, Islamic Azad University, P.O. Box 48161-19318, Sari, Iran
3Department of Mathematics, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
4Department of Mathematics and Computer Science, Faculty of Art and Sciences, Cankaya University, Yenimahalle, 06810 Ankara, Turkey
5Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia
6Institute of Space Sciences, P.O. Box, MG-23, R 76900 Magurele, Bucharest, Romania

Received 10 May 2013; Revised 11 July 2013; Accepted 1 August 2013

Academic Editor: Juan J. Trujillo

Copyright © 2013 R. Darzi 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 apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem , , , , , , where denotes Riemann-Liouville fractional derivative, ß is positive real number, , and is continuous on . As an application, one example is given to illustrate the main result.