- 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 420514, 6 pages
Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem
King Abdulaziz University, Rabigh Campus, College of Sciences and Arts, Department of Mathematics, P.O. Box 344, Rabigh 21911, Saudi Arabia
Received 4 November 2012; Accepted 25 December 2012
Academic Editor: Chuanzhi Bai
Copyright © 2013 Habib Mâagli 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.
- K. Diethelm and A. D. Freed, “On the solution of nonlinear fractional order differential equations used in the modelling of viscoplasticity,” in Scientific Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Mackens, and H. Voss, Eds., pp. 217–224, Springer, Heidelberg, Germany, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.
- W. Lin, “Global existence theory and chaos control of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 332, no. 1, pp. 709–726, 2007.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- R. P. Agarwal, D. O'Regan, and S. Staněk, “Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 371, no. 1, pp. 57–68, 2010.
- R. P. Agarwal, M. Benchohra, S. Hamani, and S. Pinelas, “Boundary value problems for differential equations involving Riemann-Liouville fractional derivative on the half-line,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 18, no. 2, pp. 235–244, 2011.
- 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.
- B. Ahmad, “Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 4, pp. 390–394, 2010.
- B. Ahmad and J. J. Nieto, “Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions,” Boundary Value Problems, vol. 2011, article 36, 2011.
- J. Caballero, J. Harjani, and K. Sadarangani, “Positive solutions for a class of singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1325–1332, 2011.
- J. Deng and L. Ma, “Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 6, pp. 676–680, 2010.
- N. Kosmatov, “A singular boundary value problem for nonlinear differential equations of fractional order,” Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp. 125–135, 2009.
- Y. Liu, W. Zhang, and X. Liu, “A sufficient condition for the existence of a positive solution for a nonlinear fractional differential equation with the Riemann-Liouville derivative,” Applied Mathematics Letters, vol. 25, no. 11, pp. 1986–1992, 2012.
- T. Qiu and Z. Bai, “Existence of positive solutions for singular fractional differential equations,” Electronic Journal of Differential Equations, vol. 149, 19 pages, 2008.
- Y. Zhao, S. Sun, Z. Han, and Q. Li, “Positive solutions to boundary value problems of nonlinear fractional differential equations,” Abstract and Applied Analysis, vol. 2011, Article ID 390543, 16 pages, 2011.
- V. Marić, Regular Variation and Differential Equations, vol. 1726 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000.
- E. Seneta, Regularly Varying Functions, vol. 508 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1976.