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Abstract and Applied Analysis
Volume 2015, Article ID 263748, 11 pages
http://dx.doi.org/10.1155/2015/263748
Research Article

Positive Solutions for Class of State Dependent Boundary Value Problems with Fractional Order Differential Operators

School of Mathematics and Physics, University of South China, Hengyang 421001, China

Received 13 April 2014; Revised 4 August 2014; Accepted 4 August 2014

Academic Editor: Ali H. Bhrawy

Copyright © 2015 Dongyuan Liu et al. 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 consider the following state dependent boundary-value problem , ; , where is the standard Riemann-Liouville fractional derivative of order , , , , the function is defined as , and the function is defined as , are continuous on and , . Using Banach contraction mapping principle and Leray-Schauder continuation principle, we obtain some sufficient conditions for the existence and uniqueness of the positive solutions for the above fractional order differential equations, which extend some references.