Positivity

, Volume 13, Issue 3, pp 583–599

Existence results of positive solutions to boundary value problem for fractional differential equation

  • Shuqin Zhang
Article

Abstract

In this paper, we consider the existence, multiplicity, and nonexistence of positive solutions to some class of boundary vale problem for fractional differential equation of high order. Our analysis relies on the fixed point index.

Keywords

Fractional differential equation positive solutions fixed point index Cone 

Mathematics Subject Classification (2000)

26A33 34B15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.A. Kilbsa, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam (2006).Google Scholar
  2. 2.
    D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl., 204(2) (1996), 609–625.Google Scholar
  3. 3.
    A.A. Kilbas, S.A. Marzan, Nonlinear differential equations in weighted spaces of continuous functions (Rusian), Dokl. Nats. Akad. Nauk Belarusi, 47(1) (2003), 29–35.Google Scholar
  4. 4.
    S. Zhang, The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., 252 (2000), 804–812.Google Scholar
  5. 5.
    S. Zhang, Positive solution for some class of nonlinear fractional differential equation, J. Math. Anal. Appl., 278(1) (2003), 136–148.Google Scholar
  6. 6.
    R. Lin, F. Liu, Fractional high order methods for the nonlinear fractional ordinary differential equation, Nonlin. Anal., 66 (2007), 856–869.Google Scholar
  7. 7.
    M. Benchohra, J. Henderson, S.K. Ntouyas, A. Ouahab, Existence results for fractional order functional differential equations with infinite delay, J. Math. Anal. Appl., 338 (2008), 1340–1350.Google Scholar
  8. 8.
    I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York (1999).Google Scholar
  9. 9.
    M. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen (1964).Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Shuqin Zhang
    • 1
  1. 1.Department of MathematicsChina University of Mining and TechnologyBeijingChina

Personalised recommendations