Skip to main content
SpringerLink
Log in

Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we investigate the existence of solutions for nonlocal boundary value problems for Riemann–Liouville fractional differential inclusions of order \({\alpha\in (1,2]}\) .

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. Agarwal R.P., Benchohra M., Hamani S.: Boundary value problems for fractional differential inclusions. Adv. Stud. Contemp. Math. 16(2), 181–196 (2008)

    MathSciNet  MATH  Google Scholar 

  2. Agarwal R.P., Benchohra M., Hamani S., Pinelas S.: Boundary value problems for differential equations involving Rieman–Liouville fractional derivative on the half line. Dyn. Contin. Discret. Impuls. Syst. 18(1), 235–244 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Agarwal R.P., Benchohra M., Hamani S.: A survey on existence results for boundary value problems for nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109(3), 973–1033 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Aubin, J.P., Cellina A.: Differential Inclusions. Springer, Berlin (1984)

  5. Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkh\({\ddot{a}}\)user, Boston (1990)

  6. Bai Z.: On positive solutions of a nonlocal fractional boundary value problem. Nonlinear Anal. 72, 916–924 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bai Z., Lu H.S.: Positive solutions of a boundary value problem of nonlinear fractional differential equation. J. Math. Anal. Appl. 311, 495–505 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Benchohra M., Djebali S., Hamani S.: Boundary value problems of differential inclusions with Riemann–Liouville fractional derivative. Nonlinear Oscil. 14(1), 7–20 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Benchohra M., Hamani S.: Nonlinear boundary value problems for differential inclusions with Caputo fractional derivative. Topol. Methods Nonlinear Anal. 32(1), 115–130 (2008)

    MathSciNet  MATH  Google Scholar 

  10. Benchohra M., Hamani S.: Boundary value problems for differential inclusions with fractional order. Discuss. Math. Differ. Incl. Control Optim. 28, 147–164 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  12. Castaing, C., Valadier, M.: Convex Analysis and Measurable Multifunctions. Lecture Notes in Mathematics, vol. 580. Springer, Berlin (1977)

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Deimling, K.: Multivalued Differential Equations. Walter De Gruyter, Berlin (1992)

  15. Delbosco D., Rodino L.: Existence and uniqueness for a nonlinear fractional differential equation. J. Math. Anal. Appl. 204, 609–625 (1996)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  17. Fryszkowski, A.: Fixed Point Theory for Decomposable Sets. Topological Fixed Point Theory and Its Applications, vol. 2. Kluwer Academic, Dordrecht (2004)

  18. Fryszkowski A.: Continuous selections for a class of nonconvex multivalued maps. Stud. Math. 76, 163174 (1983)

    MathSciNet  Google Scholar 

  19. Heymans N., Podlubny I.: Physical interpretation of initial conditions for fractional differential equations with Riemann–Liouville fractional derivatives. Rheol. Acta 45(5), 765–772 (2006)

    Article  Google Scholar 

  20. Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)

  21. Hu, S., Papageorgiou, N.: Handbook of Multivalued Analysis, Theory, vol. I. Kluwer, Dordrecht (1997)

  22. Karakostas G.L., Tsamatos P.C.: Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary value problems. Electron. J. Differ. Equ. 2002(30), 1–17 (2002)

    MathSciNet  MATH  Google Scholar 

  23. Kaufmann, E.R., Mboumi, E.: Positive solutions of a boundary value problem for a nonlinear fractional differential equation. Electron. J. Qual. Theory Differ. Equ. 3, 11 (2007)

  24. Kilbas A.A., Marzan S.A.: Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions. Differ. Equ. 41, 84–89 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier Science B.V., Amsterdam (2006)

  26. Kisielewicz, M.: Differential Inclusions and Optimal Control. Kluwer, Dordrecht (1991)

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

  28. Momani S.M., Hadid S.B.: Some comparison results for integro-fractional differential inequalities. J. Fract. Calc. 24, 37–44 (2003)

    MathSciNet  MATH  Google Scholar 

  29. Momani S.M., Hadid S.B., Alawenh Z.M.: Some analytical properties of solutions of differential equations of noninteger order. Int. J. Math. Math. Sci. 2004, 697–701 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Podlubny, I.: Fractional Differential Equation. Academic Press, San Diego (1999)

  31. Podlubny I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5, 367–386 (2002)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Mostaganem, B.P. 227, 27000, Mostaganem, Algeria

    Samira Hamani

  2. Department of Mathematics, Baylor University, Waco, TX, 76798-7328, USA

    Johnny Henderson

Authors
  1. Samira Hamani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johnny Henderson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samira Hamani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hamani, S., Henderson, J. Boundary Value Problems for Fractional Differential Inclusions with Nonlocal Conditions. Mediterr. J. Math. 13, 967–979 (2016). https://doi.org/10.1007/s00009-015-0545-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00009-015-0545-z

Mathematics Subject Classification

Keywords

Search

Navigation