Abstract and Applied Analysis
Volume 2009, Article ID 314656, 18 pages
http://dx.doi.org/10.1155/2009/314656
Research Article

## The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation

1Department of Mathematics, Xiangnan University, Chenzhou 423000, China
2School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received 13 May 2009; Accepted 23 June 2009

Copyright © 2009 Yuansheng Tian and Anping 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.

1. A. Babakhani and V. Daftardar-Gejji, “Existence of positive solutions of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 2, pp. 434–442, 2003.
2. C.-Z. Bai and J.-X. Fang, “The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations,” Applied Mathematics and Computation, vol. 150, no. 3, pp. 611–621, 2004.
3. A. M. A. El-Sayed, “Nonlinear functional-differential equations of arbitrary orders,” Nonlinear Analysis: Theory, Methods & Applications, vol. 33, no. 2, pp. 181–186, 1998.
4. V. Daftardar-Gejji and A. Babakhani, “Analysis of a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 511–522, 2004.
5. A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems—I,” Applicable Analysis, vol. 78, no. 1-2, pp. 153–192, 2001.
6. A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems—II,” Applicable Analysis, vol. 81, no. 2, pp. 435–493, 2002.
7. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
8. C. Yu and G. Gao, “Existence of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 310, no. 1, pp. 26–29, 2005.
9. S. Zhang, “The existence of a positive solution for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 252, no. 2, pp. 804–812, 2000.
10. S. Zhang, “Existence of positive solution for some class of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 1, pp. 136–148, 2003.
11. D. Delbosco and L. Rodino, “Existence and uniqueness for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 204, no. 2, pp. 609–625, 1996.
12. Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495–505, 2005.
13. D. Delbosco, “Fractional calculus and function spaces,” Journal of Fractional Calculus, vol. 6, pp. 45–53, 1994.
14. S. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, no. 36, pp. 1–12, 2006.
15. K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.