Journal of Applied Mathematics
Volume 2011 (2011), Article ID 352341, 22 pages
http://dx.doi.org/10.1155/2011/352341
Research Article

Positive Solution of Singular Fractional Differential Equation in Banach Space

Jianxin Cao1,2 and Haibo Chen1

1Department of Mathematics, Central South University, Changsha, Hunan 410075, China
2Faculty of Science, Hunan Institute of Engineering, Xiangtan, Hunan 411104, China

Received 17 June 2011; Accepted 9 September 2011

Academic Editor: J. Biazar

Copyright © 2011 Jianxin Cao and Haibo Chen. 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 investigated a singular multipoint boundary value problem for fractional differential equation in Banach space. The nonlinear term 𝑓 ( 𝑡 , 𝑥 , 𝑦 ) is positive and singular at 𝑥 = 𝜃 and (or) 𝑦 = 𝜃 . Employing regularization, sequential techniques, and diagonalization methods, we obtained some new existence results of positive solution.