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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 512426, 18 pages
Research Article

Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator

School of Mathematics Science, University of Electronic Science and Technology of China, Chengdu 611731, China

Received 28 February 2014; Accepted 26 April 2014; Published 15 May 2014

Academic Editor: Bashir Ahmad

Copyright © 2014 Min Jiang and Shouming Zhong. 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.


This paper investigates the existence, multiplicity, nonexistence, and uniqueness of positive solutions to a kind of two-point boundary value problem for nonlinear fractional differential equations with -Laplacian operator. By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations with -Laplacian operator in terms of different value of parameter. In particular, the dependence of positive solution on the parameter was obtained. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable.