- 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 2013 (2013), Article ID 493164, 8 pages
Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China
Received 27 April 2013; Accepted 7 August 2013
Academic Editor: Yong Zhou
Copyright © 2013 Chaozhu Hu 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.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- V. Lakshmikantham, S. Leela, and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, Mass, USA, 2009.
- Q. M. Al-Mdallal, “On the numerical solution of fractional Sturm-Liouville problems,” International Journal of Computer Mathematics, vol. 87, no. 12, pp. 2837–2845, 2010.
- S. Momani and Z. Odibat, “Analytical approach to linear fractional partial differential equations arising in fluid mechanics,” Physics Letters A, vol. 355, pp. 271–279, 2006.
- S. Momani and N. Shawagfeh, “Decomposition method for solving fractional Riccati differential equations,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1083–1092, 2006.
- Q. M. Al-Mdallal, M. I. Syam, and M. N. Anwar, “A collocation-shooting method for solving fractional boundary value problems,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3814–3822, 2010.
- F. Jiao and Y. Zhou, “Existence results for fractional boundary value problem via critical point theory,” International Journal of Bifurcation and Chaos, vol. 22, no. 4, Article ID 1250086, 2012.
- F. Jiao and Y. Zhou, “Existence of solutions for a class of fractional boundary value problems via critical point theory,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1181–1199, 2011.
- C. F. Li, X. N. Luo, and Y. Zhou, “Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1363–1375, 2010.
- S. Abbas and M. Benchohra, “Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order,” Nonlinear Analysis: Hybrid Systems, vol. 4, no. 3, pp. 406–413, 2010.
- M. Benchohra and S. Hamani, “The method of upper and lower solutions and impulsive fractional differential inclusions,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 433–440, 2009.
- A. Shi and S. Zhang, “Upper and lower solutions method and a fractional differential equation boundary value problem,” Electronic Journal of Qualitative Theory of Differential Equations, vol. 30, pp. 1–13, 2009.
- G. Wang, “Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments,” Journal of Computational and Applied Mathematics, vol. 236, no. 9, pp. 2425–2430, 2012.
- M. Al-Refai and M. Ali Hajji, “Monotone iterative sequences for nonlinear boundary value problems of fractional order,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 11, pp. 3531–3539, 2011.
- H. L. Royden, Real Analysis, Macmillan Publishing Company, New York, NY, USA, 3rd edition, 1988.