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Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions

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  • Ahmad, Bashir
  • K. Ntouyas, Sotiris

Abstract

This paper is concerned with the existence and uniqueness of solutions for a coupled system of Caputo type sequential fractional differential equations supplemented with nonlocal Riemann–Liouville integral boundary conditions. The existence of solutions is derived by applying Leray–Schauder’s alternative, while the uniqueness of solution is established via Banach’s contraction principle. An illustrative example is also included. The paper concludes with some interesting observations.

Suggested Citation

  • Ahmad, Bashir & K. Ntouyas, Sotiris, 2015. "Existence results for a coupled system of Caputo type sequential fractional differential equations with nonlocal integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 615-622.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:615-622
    DOI: 10.1016/j.amc.2015.05.116
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    Citations

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    Cited by:

    1. Bashir Ahmad & Ahmed Alsaedi & Sotiris K. Ntouyas & Hamed H. Al-Sulami, 2019. "On Neutral Functional Differential Inclusions involving Hadamard Fractional Derivatives," Mathematics, MDPI, vol. 7(11), pages 1-13, November.
    2. Nazim I Mahmudov & Sameer Bawaneh & Areen Al-Khateeb, 2019. "On a Coupled System of Fractional Differential Equations with Four Point Integral Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    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.
    4. Nazim I Mahmudov & Areen Al-Khateeb, 2019. "Stability, Existence and Uniqueness of Boundary Value Problems for a Coupled System of Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
    5. Ahmad, Bashir & Ntouyas, Sotiris K. & Alsaedi, Ahmed, 2016. "On a coupled system of fractional differential equations with coupled nonlocal and integral boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 234-241.
    6. Agarwal, Ravi P. & Ahmad, Bashir & Garout, Doa’a & Alsaedi, Ahmed, 2017. "Existence results for coupled nonlinear fractional differential equations equipped with nonlocal coupled flux and multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 149-161.
    7. Abdelkader Moumen & Abdelaziz Mennouni & Mohamed Bouye, 2023. "A Novel Vieta–Fibonacci Projection Method for Solving a System of Fractional Integrodifferential Equations," Mathematics, MDPI, vol. 11(18), pages 1-14, September.
    8. Liu, Xiping & Jia, Mei, 2019. "Solvability and numerical simulations for BVPs of fractional coupled systems involving left and right fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 230-242.
    9. 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.
    10. Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad & Shahram Rezapour & Jessada Tariboon, 2022. "Sequential Fractional Hybrid Inclusions: A Theoretical Study via Dhage’s Technique and Special Contractions," Mathematics, MDPI, vol. 10(12), pages 1-27, June.
    11. Jarunee Soontharanon & Saowaluck Chasreechai & Thanin Sitthiwirattham, 2019. "A Coupled System of Fractional Difference Equations with Nonlocal Fractional Sum Boundary Conditions on the Discrete Half-Line," Mathematics, MDPI, vol. 7(3), pages 1-22, March.
    12. Almalahi, Mohammed A. & Panchal, Satish K. & Jarad, Fahd, 2021. "Stability results of positive solutions for a system of ψ -Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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