About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 723507, 17 pages
http://dx.doi.org/10.1155/2012/723507
Research Article

Existence of Positive Solution for Semipositone Fractional Differential Equations Involving Riemann-Stieltjes Integral Conditions

1Water Transportation Planning & Logistics Engineering Institute, College of Harbor, Coastal and Offshore Engineering, Hohai University, Jiangsu, Nanjing 210098, China
2National Research Center for Resettlement, Hohai University, Jiangsu, Nanjing 210098, China

Received 13 May 2012; Accepted 11 July 2012

Academic Editor: Yong Hong Wu

Copyright © 2012 Wei Wang and Li Huang. 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. W. G. Glockle and T. F. Nonnenmacher, “A fractional calculus approach of self-similar protein dynamics,” Biophysical Journal, vol. 68, no. 1, pp. 46–53, 1995. View at Publisher · View at Google Scholar
  2. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, River Edge, NJ, USA, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. F. Metzler, W. Schick, H. G. Kilian, and T. F. Nonnenmache, “Relaxation in filled polymers: a fractional calculus approach,” Journal of Chemical Physics, vol. 103, no. 16, pp. 7180–7186, 1995.
  4. I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, London, UK, 1999. View at Zentralblatt MATH
  5. I. Podlubny, “Geometric and physical interpretation of fractional integration and fractional differentiation,” Fractional Calculus & Applied Analysis, vol. 5, no. 4, pp. 367–386, 2002. View at Zentralblatt MATH
  6. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
  7. V. Lakshmikantham, S. Leela, and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, UK, 2009.
  8. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and derivatives Theory and Applications, Gordon and Breach Science Publishers, Yverdon-les-Bains, Switzerland, 1993.
  9. R. P. Agarwal, M. Benchohra, and S. Hamani, “A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 973–1033, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. X. Zhang, L. Liu, and Y. Wu, “The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives,” Applied Mathematics and Computation, vol. 218, no. 17, pp. 8526–8536, 2012.
  11. X. Zhang, L. Liu, B. Wiwatanapataphee, and Y. Wu, “Positive solutions of eigenvalue problems for a class of fractional differential equations with derivatives,” Abstract and Applied Analysis, vol. 2012, Article ID Article ID 512127, 16 pages, 2012. View at Publisher · View at Google Scholar
  12. X. Zhang, L. Liu, and Y. Wu, “Multiple positive solutions of a singular fractional differential equation with negatively perturbed term,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 1263–1274, 2012.
  13. Y. Wang, L. Liu, and Y. Wu, “Positive solutions of a fractional boundary value problem with changing sign nonlinearity,” Abstract and Applied Analysis, vol. 2012, Article ID 149849, 12 pages, 2012. View at Publisher · View at Google Scholar
  14. X. Zhang, L. Liu, and Y. Wu, “Existence results for multiple positive solutions of nonlinear higher orderperturbed fractional differential equations with derivatives,” Applied Mathematics and Computation, http://dx.doi.org/10.1016/j.amc.2012.07.046.
  15. J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems involving integral conditions,” Nonlinear Differential Equations and Applications, vol. 15, no. 1-2, pp. 45–67, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. J. R. L. Webb and G. Infante, “Positive solutions of nonlocal boundary value problems: a unified approach,” Journal of the London Mathematical Society, vol. 74, no. 3, pp. 673–693, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. J. R. L. Webb, “Nonlocal conjugate type boundary value problems of higher order,” Nonlinear Analysis. Theory, Methods & Applications, vol. 71, no. 5-6, pp. 1933–1940, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. X. Hao, L. Liu, Y. Wu, and Q. Sun, “Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions,” Nonlinear Analysis. Theory, Methods & Applications, vol. 73, no. 6, pp. 1653–1662, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. 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
  20. C. S. Goodrich, “Existence of a positive solution to a class of fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1050–1055, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. M. Rehman and R. A. Khan, “Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations,” Applied Mathematics Letters, vol. 23, no. 9, pp. 1038–1044, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. Y. Wang, L. Liu, and Y. Wu, “Positive solutions for a nonlocal fractional differential equation,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 11, pp. 3599–3605, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. X. Zhang and Y. Han, “Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations,” Applied Mathematics Letters, vol. 25, no. 3, pp. 555–560, 2012. View at Publisher · View at Google Scholar
  24. R. Aris, Introduction to the Analysis of Chemical Reactors, Prentice Hall, Englewood Cliffs, NJ, USA, 1965.
  25. X. Zhang and L. Liu, “Positive solutions of superlinear semipositone singular Dirichlet boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 316, no. 2, pp. 525–537, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. Y. Wang, L. Liu, and Y. Wu, “Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity,” Nonlinear Analysis. Theory, Methods & Applications, vol. 74, no. 17, pp. 6434–6441, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, New York, NY, USA, 1988.