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Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives

Author

Listed:
  • Johnny Henderson

    (Department of Mathematics, Baylor University, Waco, TX 76798-7328, USA)

  • Rodica Luca

    (Department of Mathematics, Gh. Asachi Technical University, 11 Blvd. Carol I, 700506 Iasi, Romania)

  • Alexandru Tudorache

    (Department of Computer Science and Engineering, Gh. Asachi Technical University, 700050 Iasi, Romania)

Abstract

We study the existence and multiplicity of positive solutions for a system of Riemann–Liouville fractional differential equations with sequential derivatives, positive parameters and sign-changing singular nonlinearities, subject to nonlocal coupled boundary conditions which contain Riemann–Stieltjes integrals and various fractional derivatives. In the proof of our main existence results we use the nonlinear alternative of Leray–Schauder type and the Guo–Krasnosel’skii fixed point theorem.

Suggested Citation

  • Johnny Henderson & Rodica Luca & Alexandru Tudorache, 2021. "Positive Solutions for a System of Coupled Semipositone Fractional Boundary Value Problems with Sequential Fractional Derivatives," Mathematics, MDPI, vol. 9(7), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:753-:d:527846
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    References listed on IDEAS

    as
    1. Henderson, Johnny & Luca, Rodica, 2017. "Systems of Riemann–Liouville fractional equations with multi-point boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 303-323.
    2. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
    3. Ahmad, Bashir & Luca, Rodica, 2017. "Existence of solutions for a sequential fractional integro-differential system with coupled integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 378-388.
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