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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 728491, 9 pages
http://dx.doi.org/10.1155/2015/728491
Research Article

Monotone and Concave Positive Solutions to Three-Point Boundary Value Problems of Higher-Order Fractional Differential Equations

College of Mathematics and Statistics, Jishou University, 120 Renmin South Road, Jishou, Hunan 416000, China

Received 26 June 2014; Accepted 21 August 2014

Academic Editor: Wei-Shih Du

Copyright © 2015 Wenyong Zhong and Lanfang Wang. 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 study the three-point boundary value problem of higher-order fractional differential equations of the form , , , , , where is the Caputo fractional derivative of order , and the function is continuously differentiable. Here, , , . By virtue of some fixed point theorems, some sufficient criteria for the existence and multiplicity results of positive solutions are established and the obtained results also guarantee that the positive solutions discussed are monotone and concave.