Skip to main content
SpringerLink
Log in

Existence of Nonnegative Solutions for a Fractional Integro-Differential Equation

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

We investigate the existence of nonnegative solutions for a fractional integro-differential equation subject to multi-point boundary conditions, by using the Banach contraction mapping principle and the Krasnosel’skii fixed point theorem for the sum of two operators.

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., Nieto, J.J.: Boundary value problems for a class of sequential integrodifferential equations of fractional order. J. Funct. Spaces Appl. 2013, 149659-1–149659-8 (2013)

  2. Aljoudi, S., Ahmad, B., Nieto, J.J., Alsaedi, A.: A coupled system of Hadamard type sequential fractional differential equations with coupled strip conditions. Chaos Solitons Fractals 91, 39–46 (2016)

    Article  MathSciNet  Google Scholar 

  3. Burton, T.A.: A fixed point theorem of Krasnoselskii. Appl. Math. Lett. 11(1), 85–88 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. Caballero, J., Cabrera, I., Sadarangani, K.: Positive solutions of nonlinear fractional differential equations with integral boundary value conditions. Abstr. Appl. Anal. 2012, 303545-1–303545-11 (2012)

  5. Das, S.: Functional Fractional Calculus for System Identification and Controls. Springer, New York (2008)

    MATH  Google Scholar 

  6. Graef, J.R., Kong, L., Kong, Q., Wang, M.: Uniqueness of positive solutions of fractional boundary value problems with non-homogeneous integral boundary conditions. Fract. Calc. Appl. Anal. 15(3), 509–528 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Henderson, J., Luca, R.: Boundary Value Problems for Systems of Differential, Difference and Fractional Equations. Positive Solutions. Elsevier, Amsterdam (2016)

    MATH  Google Scholar 

  8. Henderson, J., Luca, R.: Existence of positive solutions for a singular fractional boundary value problem. Nonlinear Anal. Model. Control 22(1), 99–114 (2017)

    MathSciNet  Google Scholar 

  9. Henderson, J., Luca, R., Tudorache, A.: On a system of fractional differential equations with coupled integral boundary conditions. Fract. Calc. Appl. Anal. 18(2), 361–386 (2015)

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  11. Krasnosel’skii, M.A.: Some problems of nonlinear analysis. Am. Math. Soc. Trans. 10(2), 345–409 (1958)

    MathSciNet  Google Scholar 

  12. Luca, R., Tudorache, A.: Positive solutions to a system of semipositone fractional boundary value problems. Adv. Differ. Equ. 2014(179), 1–11 (2014)

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  14. Sabatier, J., Agrawal, O.P., Machado, J.A.T. (eds.): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)

    MATH  Google Scholar 

  15. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon (1993)

    MATH  Google Scholar 

  16. Smart, D.R.: Fixed Point Theorems. Cambridge Univ. Press, Cambridge (1980)

    MATH  Google Scholar 

  17. Wang, Y., Liu, L.: Uniqueness and existence of positive solutions for the fractional integro-differential equation. Bound. Value Probl. 2017(12), 1–17 (2017)

    MathSciNet  Google Scholar 

  18. Yuan, C.: Two positive solutions for \((n - 1,1)\)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17(2), 930–942 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Johnny Henderson

  2. Department of Mathematics, Gh. Asachi Technical University, 700506, Iasi, Romania

    Rodica Luca

Authors
  1. Johnny Henderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodica Luca
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rodica Luca.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Henderson, J., Luca, R. Existence of Nonnegative Solutions for a Fractional Integro-Differential Equation. Results Math 72, 747–763 (2017). https://doi.org/10.1007/s00025-017-0655-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00025-017-0655-y

Mathematics Subject Classification

Keywords

Search

Navigation