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Abstract and Applied Analysis
Volume 2014, Article ID 537971, 9 pages
http://dx.doi.org/10.1155/2014/537971
Research Article

Existence and Global Asymptotic Behavior of Positive Solutions for Nonlinear Fractional Dirichlet Problems on the Half-Line

1College of Sciences, Mathematics Department, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
2College of Sciences and Arts, Department of Mathematics, King Abdulaziz University, Ragigh Campus, P.O. Box 344, Rabigh 21911, Saudi Arabia

Received 4 April 2014; Accepted 17 June 2014; Published 16 July 2014

Academic Editor: Mohamed Boussairi Jleli

Copyright © 2014 Imed Bachar and Habib Mâagli. 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 are interested in the following fractional boundary value problem: , , , , where , , is the standard Riemann-Liouville fractional derivative, and is a nonnegative continuous function on satisfying some appropriate assumptions related to Karamata regular variation theory. Using the Schauder fixed point theorem, we prove the existence and the uniqueness of a positive solution. We also give a global behavior of such solution.