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Journal of Function Spaces and Applications
Volume 2013, Article ID 585639, 9 pages
http://dx.doi.org/10.1155/2013/585639
Research Article

Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space

Department of Mathematics, Shandong Normal University, Jinan 250014, China

Received 29 May 2013; Accepted 11 July 2013

Academic Editor: William P. Ziemer

Copyright © 2013 Bo Liu 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.

Abstract

This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. Finally, an illustrative example is given to support the obtained new results.