Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015, Article ID 736108, 6 pages
http://dx.doi.org/10.1155/2015/736108
Research Article

Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

1Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
2Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Received 16 July 2015; Accepted 14 September 2015

Academic Editor: Chris Goodrich

Copyright © 2015 Jun-Rui Yue 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. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.
  2. W. Feng, S. Sun, X. Li, and M. Xu, “Positive solutions to fractional boundary value problems with nonlinear boundary conditions,” Boundary Value Problems, vol. 2014, article 225, 2014. View at Publisher · View at Google Scholar · View at Scopus
  3. D. Q. Jiang and C. J. Yuan, “The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application,” Nonlinear Analysis, Theory, Methods and Applications, vol. 72, no. 2, pp. 710–719, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. Z.-W. Lv, “Positive solutions of m-point boundary value problems for fractional differential equations,” Advances in Difference Equations, vol. 2011, Article ID 571804, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. W. G. Yang, “Positive solutions for nonlinear Caputo fractional differential equations with integral boundary conditions,” Journal of Applied Mathematics and Computing, vol. 44, no. 1-2, pp. 39–59, 2014. View at Publisher · View at Google Scholar · View at Scopus
  6. S. Q. Zhang, “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 2006, article 36, 12 pages, 2006. View at Google Scholar
  7. Y. D. Ji, Y. P. Guo, J. Q. Qiu, and L. Y. Yang, “Existence of positive solutions for a boundary value problem of nonlinear fractional differential equations,” Advances in Difference Equations, vol. 2015, article 13, 2015. View at Publisher · View at Google Scholar · View at Scopus
  8. C. F. Li, X. N. Luo, and Y. Zhou, “Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations,” Computers and Mathematics with Applications, vol. 59, no. 3, pp. 1363–1375, 2010. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Z. Xie, J. Xiao, and Z. G. Luo, “Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions,” Applied Mathematics Letters, vol. 41, pp. 46–51, 2015. View at Publisher · View at Google Scholar · View at Scopus
  10. J. F. Xu, Z. L. Wei, and W. Dong, “Uniqueness of positive solutions for a class of fractional boundary value problems,” Applied Mathematics Letters, vol. 25, no. 3, pp. 590–593, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. K. Zhao and P. Gong, “Existence of positive solutions for a class of higher-order Caputo fractional differential equation,” Qualitative Theory of Dynamical Systems, vol. 14, no. 1, pp. 157–171, 2015. View at Publisher · View at Google Scholar
  12. Z. B. Bai and T. T. Qiu, “Existence of positive solution for singular fractional differential equation,” Applied Mathematics and Computation, vol. 215, no. 7, pp. 2761–2767, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. X. Q. Zhang, L. Wang, and Q. Sun, “Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter,” Applied Mathematics and Computation, vol. 226, pp. 708–718, 2014. View at Publisher · View at Google Scholar · View at Scopus
  14. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, NY, USA, 1988.
  15. M. A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen, The Netherlands, 1964.