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The Scientific World Journal
Volume 2013, Article ID 473828, 9 pages
Research Article

Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems

School of Mathematical Sciences, Shandong Normal University, Jinan, Shandong 250014, China

Received 23 August 2013; Accepted 19 September 2013

Academic Editors: A. Atangana, A. Kilicman, S. C. O. Noutchie, S. S. Ray, and A. Secer

Copyright © 2013 Daliang Zhao and Yansheng Liu. 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 is devoted to the existence of multiple positive solutions for fractional boundary value problem , , , where is a real number, is the Caputo fractional derivative, and is continuous. Firstly, by constructing a special cone, applying Guo-Krasnoselskii’s fixed point theorem and Leggett-Williams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii’s fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results.