Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 898206, 12 pages
http://dx.doi.org/10.1155/2013/898206
Research Article

Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with -Laplacian Operator

1Basic Science Department, Qingdao Binhai University, Qingdao 266555, China
2School of Control Science and Engineering, Shandong University, Jinan 250061, China

Received 13 August 2013; Accepted 23 September 2013

Academic Editors: S. Cingolani, C. Gutiérrez, G. Lu, and M. McKibben

Copyright © 2013 Xiangshan Kong and Haitao Li. 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

This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with -Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective.