Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 129640, 7 pages
http://dx.doi.org/10.1155/2013/129640
Research Article

Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations

1College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China
2School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received 25 March 2013; Accepted 20 May 2013

Academic Editor: Yonghong Wu

Copyright © 2013 Zhanbing Bai 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. 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
  2. R. P. Agarwal, D. O'Regan, and S. Staněk, “Positive solutions for mixed problems of singular fractional differential equations,” Mathematische Nachrichten, vol. 285, no. 1, pp. 27–41, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. Ahmad and J. J. Nieto, “Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions,” Boundary Value Problems, vol. 2009, Article ID 708576, 11 pages, 2009. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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
  5. Z. Bai, “On positive solutions of a nonlocal fractional boundary value problem,” Nonlinear Analysis: Theory, Methods & Applications, vol. 72, no. 2, pp. 916–924, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Z. Bai and W. Sun, “Existence and multiplicity of positive solutions for singular fractional boundary value problems,” Computers & Mathematics with Applications, vol. 63, no. 9, pp. 1369–1381, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. Benchohra, S. Hamani, and S. K. Ntouyas, “Boundary value problems for differential equations with fractional order and nonlocal conditions,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2391–2396, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. K. Chang and J. J. Nieto, “Some new existence results for fractional differential inclusions with boundary conditions,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 605–609, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Feng, S. Sun, Z. Han, and Y. Zhao, “Existence of solutions for a singular system of nonlinear fractional differential equations,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1370–1378, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. 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 B.V., Amsterdam, The Netherlands, 2006. View at MathSciNet
  11. X. Liu and M. Jia, “Multiple solutions for fractional differential equations with nonlinear boundary conditions,” Computers & Mathematics with Applications, vol. 59, no. 8, pp. 2880–2886, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Wang, Y. Zhou, and W. Wei, “A class of fractional delay nonlinear integrodifferential controlled systems in Banach spaces,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4049–4059, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Z. Wei, W. Dong, and J. Che, “Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative,” Nonlinear Analysis: Theory, Methods & Applications, vol. 73, no. 10, pp. 3232–3238, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. 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
  16. 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
  17. D. R. Smart, Fixed Point Theorems, Cambridge University Press, Cambridge, UK, 1980. View at MathSciNet