- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 605614, 9 pages
Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation
Department of Mathematics, Shandong University of Science and Technology, Qingdao 266510, China
Received 27 December 2010; Revised 2 March 2011; Accepted 3 March 2011
Academic Editor: Elena Braverman
Copyright © 2011 Yujun Cui. 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.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science, Amsterdam, The Netherlands, 2006.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, John Wiley & Sons, New York, NY, USA, 1993.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- S. Zhang, “Existence of solution for a boundary value problem of fractional order,” Acta Mathematica Scientia, vol. 26, no. 2, pp. 220–228, 2006.
- 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.
- X. Xu, D. Jiang, and C. Yuan, “Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 10, pp. 4676–4688, 2009.
- J. A. Gatica, V. Oliker, and P. Waltman, “Singular nonlinear boundary value problems for second-order ordinary differential equations,” Journal of Differential Equations, vol. 79, no. 1, pp. 62–78, 1989.
- J. Henderson and W. Yin, “Singular boundary value problems between conjugate and right focal,” Journal of Computational and Applied Mathematics, vol. 88, no. 1, pp. 57–69, 1998.
- P. W. Eloe and J. Henderson, “Singular nonlinear conjugate boundary value problems,” Journal of Differential Equations, vol. 133, no. 1, pp. 136–151, 1997.
- P. W. Eloe and J. Henderson, “Singular nonlinear multipoint conjugate boundary value problems,” Communications in Applied Analysis, vol. 2, no. 4, pp. 497–511, 1998.
- J. J. DaCunha, J. M. Davis, and P. K. Singh, “Existence results for singular three point boundary value problems on time scales,” Journal of Mathematical Analysis and Applications, vol. 295, no. 2, pp. 378–391, 2004.
- Y. Feng and S. Liu, “Solvability of a third-order two-point boundary value problem,” Applied Mathematics Letters, vol. 18, no. 9, pp. 1034–1040, 2005.
- Q. Yao and Y. Feng, “The existence of solution for a third-order two-point boundary value problem,” Applied Mathematics Letters, vol. 15, no. 2, pp. 227–232, 2002.
- K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
- D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, vol. 5 of Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988.