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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 728491, 9 pages
http://dx.doi.org/10.1155/2015/728491
Research Article

Monotone and Concave Positive Solutions to Three-Point Boundary Value Problems of Higher-Order Fractional Differential Equations

College of Mathematics and Statistics, Jishou University, 120 Renmin South Road, Jishou, Hunan 416000, China

Received 26 June 2014; Accepted 21 August 2014

Academic Editor: Wei-Shih Du

Copyright © 2015 Wenyong Zhong and Lanfang Wang. 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. K. B. Oldham and J. Spanier, Fractional Calculus Theory and Applications, Differentiation and Integration to Arbitrary Order, Academic Press, New York, NY, USA, 1974.
  2. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integral and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
  3. 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
  4. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, Calif, USA, 1999. View at MathSciNet
  5. W. Y. Zhong and W. Lin, “Nonlocal and multiple-point boundary value problem for fractional differential equations,” Computers & Mathematics with Applications, vol. 59, no. 3, pp. 1345–1351, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. W. Zhong, “Positive solutions for multipoint boundary value problem of fractional differential equations,” Abstract and Applied Analysis, vol. 2010, Article ID 601492, 15 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Wang, H. Xiang, and Y. Zhao, “Monotone and concave positive solutions to a boundary value problem for higher-order fractional differential equation,” Abstract and Applied Analysis, vol. 2011, Article ID 430457, 14 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. C. S. Goodrich, “On a fractional boundary value problem with fractional boundary conditions,” Applied Mathematics Letters, vol. 25, no. 8, pp. 1101–1105, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. N. Nyamoradi, “Existence of solutions for multi point boundary value problems for fractional differential equations,” Arab Journal of Mathematical Sciences, vol. 18, no. 2, pp. 165–175, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. A. Cabada and G. T. Wang, “Positive solutions of nonlinear fractional differential equations with integral boundary value conditions,” Journal of Mathematical Analysis and Applications, vol. 389, no. 1, pp. 403–411, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. Y. Zhou, “Advances in fractional differential equations, III,” Computers & Mathematics with Applications, vol. 64, no. 10, p. 2965, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. S. Vong, “Positive solutions of singular fractional differential equations with integral boundary conditions,” Mathematical and Computer Modelling, vol. 57, no. 5-6, pp. 1053–1059, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. W. H. Jiang, “Nonlinear fractional differential equations with integral boundary value conditions original,” Applied Mathematics and Computation, vol. 219, pp. 4570–4575, 2013. View at Google Scholar
  14. M. Jia and X. Liu, “Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions,” Applied Mathematics and Computation, vol. 232, pp. 313–323, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. A. Cabada and Z. Hamdi, “Nonlinear fractional differential equations with integral boundary value conditions,” Applied Mathematics and Computation, vol. 228, pp. 251–257, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. İ. Yaslan, “Existence of positive solutions for nonlinear three-point problems on time scales,” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 888–897, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. Z. He and L. Li, “Multiple positive solutions for the one-dimensional p-Laplacian dynamic equations on time scales,” Mathematical and Computer Modelling, vol. 45, no. 1-2, pp. 68–79, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. R. I. Avery and J. Henderson, “Two positive fixed points of nonlinear operators on ordered Banach spaces,” Communications on Applied Nonlinear Analysis, vol. 8, no. 1, pp. 27–36, 2001. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. I. Avery, “A generalization of the Leggett-Williams fixed point theorem,” Mathematical Sciences Research Hot-Line, vol. 3, no. 7, pp. 9–14, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet