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Abstract and Applied Analysis
Volume 2011, Article ID 430457, 14 pages
http://dx.doi.org/10.1155/2011/430457
Research Article

Monotone and Concave Positive Solutions to a Boundary Value Problem for Higher-Order Fractional Differential Equation

1Department of Mathematics, Xiangnan University, Chenzhou 423000, China
2School of Mathematics and Computational Science, Sun-Yat Sen University, Guangzhou 510275, China

Received 31 March 2011; Accepted 14 July 2011

Academic Editor: K. Chang

Copyright © 2011 Jinhua Wang 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 boundary value problem for nonlinear fractional differential equation 𝐷𝛼0+𝑢(𝑡)+𝑓(𝑡,𝑢(𝑡))=0,0<𝑡<1,𝑛1<𝛼𝑛,𝑛>3,𝑢(0)=𝑢(1)=𝑢(0)==𝑢(𝑛1)(0)=0, where 𝐷𝛼0+ denotes the Caputo fractional derivative. By using fixed point theorem, we obtain some new results for the existence and multiplicity of solutions to a higher-order fractional boundary value problem. The interesting point lies in the fact that the solutions here are positive, monotone, and concave.