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Abstract and Applied Analysis
Volume 2014, Article ID 120781, 7 pages
http://dx.doi.org/10.1155/2014/120781
Research Article

Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

Department of Mathematics, College of Sciences and Arts, King Abdulaziz University, Rabigh Campus, P.O. Box 344, Rabigh 21911, Saudi Arabia

Received 25 December 2013; Accepted 14 February 2014; Published 1 April 2014

Academic Editor: Samir Saker

Copyright © 2014 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.

Linked References

  1. S. Abbas, M. Benchohra, and G. M. N'Guérékata, Topics in Fractional Differential Equations, Developments in Mathematics, Springer, New York, NY, USA, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  2. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. T. Qiu and Z. Bai, “Existence of positive solutions for singular fractional differential equations,” Electronic Journal of Differential Equations, vol. 149, p. 19, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Staněk, “The existence of positive solutions of singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1379–1388, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. Zhang, “Positive solutions to singular boundary value problem for nonlinear fractional differential equation,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1300–1309, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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. View at Google Scholar
  13. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.
  14. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  16. V. Marić, Regular Variation and Differential Equations, vol. 1726 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  17. E. Seneta, Regularly Varying Functions, vol. 508 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1976. View at MathSciNet