Skip to main content
SpringerLink
Log in

On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

The existence of solutions of an anti-periodic boundary value problem for fractional differential inclusions of order α∈(2,3] is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahmad, B.: Existence of solutions for fractional differential equations of order q∈(2,3] with anti-periodic boundary conditions. J. Appl. Math. Comput. doi:10.1007/s12190-009-0328-4

  2. Ahmad, B., Otero-Espinar, V.: Existence of solutions for functional differential inclusions with antiperiodic boundary conditions. Bound. Value Probl. 2009, 625347 (2009)

    MathSciNet  Google Scholar 

  3. Ait Dads, E., Benchohra, M., Hamani, S.: Impulsive fractional differential inclusions involving Caputo fractional derivative. Fract. Calc. Appl. Anal. 12, 15–38 (2009)

    MATH  MathSciNet  Google Scholar 

  4. Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Existence results for fractional order functional differential equations with infinite delay. J. Math. Anal. Appl. 338, 1340–1350 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Benchohra, M., Henderson, J., Ntouyas, S.K., Ouahab, A.: Existence results for fractional order functional differential inclusions with infinite delay and applications to control theory. Fract. Calc. Appl. Anal. 11, 35–56 (2008)

    MATH  MathSciNet  Google Scholar 

  6. Bressan, A., Colombo, G.: Extensions and selections of maps with decomposable values. Stud. Math. 90, 69–86 (1988)

    MATH  MathSciNet  Google Scholar 

  7. Caputo, M.: Elasticità e Dissipazione. Zanichelli, Bologna (1969)

    Google Scholar 

  8. Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Springer, Berlin (1977)

    MATH  Google Scholar 

  9. Cernea, A.: On the existence of solutions for fractional differential inclusions with boundary conditions. Fract. Calc. Appl. Anal. 12, 433–442 (2009)

    MATH  MathSciNet  Google Scholar 

  10. Cernea, A.: Continuous version of Filippov’s theorem for fractional differential inclusions. Nonlinear Anal. 72, 204–208 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  11. Cernea, A.: On the existence of solutions for nonconvex fractional hyperbolic differential inclusions. Commun. Math. Anal. 9, 109–120 (2010)

    MATH  MathSciNet  Google Scholar 

  12. Chang, Y.K., Nieto, J.J.: Some new existence results for fractional differential inclusions with boundary conditions. Math. Comput. Model. 49, 605–609 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Chu, J., Li, M.: Positive periodic solutions of Hills equations with singular nonlinear perturbations. Nonlinear Anal. 69, 276–286 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  14. Chu, J., Nieto, J.J.: Impulsive periodic solutions of first-order singular differential equations. Bull. Lond. Math. Soc. 40, 143–150 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chu, J., Torres, P.J., Zhang, M.: Periodic solutions of second-order non-autonomous singular dynamical systems. J. Differ. Equ. 239, 196–212 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  16. Covitz, H., Nadler, S.B. Jr.: Multivalued contraction mapping in generalized metric spaces. Isr. J. Math. 8, 5–11 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  17. El-Sayed, A.M.A., Ibrahim, A.G.: Multivalued fractional differential equations of arbitrary orders. Appl. Math. Comput. 68, 15–25 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. Frignon, M., Granas, A.: Théorèmes d’existence pour les inclusions différentielles sans convexité. C. R. Acad. Sci. Paris, Ser. I 310, 819–822 (1990)

    Google Scholar 

  19. Henderson, J., Ouahab, A.: Fractional functional differential inclusions with finite delay. Nonlinear Anal. 70, 2091–2105 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Jiang, D., Chu, J., Zhang, M.: Multiplicity of positive periodic solutions to superlinear repulsive singular equations. J. Differ. Equ. 211, 282–302 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  21. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)

    MATH  Google Scholar 

  22. Lasota, A., Opial, Z.: An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations. Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 13, 781–786 (1965)

    MATH  MathSciNet  Google Scholar 

  23. Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Differential Equations. Wiley, New York (1993)

    MATH  Google Scholar 

  24. O’Regan, D.: Fixed point theory for closed multifunctions. Arch. Math. (Brno) 34, 191–197 (1998)

    MATH  MathSciNet  Google Scholar 

  25. Ouahab, A.: Some results for fractional boundary value problem of differential inclusions. Nonlinear Anal. 69, 3871–3896 (2009)

    Google Scholar 

  26. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14, 010014, Bucharest, Romania

    Aurelian Cernea

Authors
  1. Aurelian Cernea
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aurelian Cernea.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cernea, A. On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions. J. Appl. Math. Comput. 38, 133–143 (2012). https://doi.org/10.1007/s12190-010-0468-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-010-0468-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation