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Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and Integrals

Author

Listed:
  • Muthaiah Subramanian

    (Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, India
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Deparment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Turkey
    These authors contributed equally to this work.)

  • Mohamed I. Abbas

    (Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

Abstract

In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete and integral boundary conditions. The nonlinearity relies both on the unknown functions and their fractional derivatives and integrals in the lower order. The consequence of existence is obtained utilizing the alternative of Leray–Schauder, while the result of uniqueness is based on the concept of Banach contraction mapping. We introduced the concept of unification in the present work with varying parameters of the multi-point and classical integral boundary conditions. With the help of examples, the main results are well demonstrated.

Suggested Citation

  • Muthaiah Subramanian & Jehad Alzabut & Mohamed I. Abbas & Chatthai Thaiprayoon & Weerawat Sudsutad, 2022. "Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and," Mathematics, MDPI, vol. 10(11), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1823-:d:824053
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    References listed on IDEAS

    as
    1. Ge, Zheng-Ming & Ou, Chan-Yi, 2008. "Chaos synchronization of fractional order modified duffing systems with parameters excited by a chaotic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 705-717.
    2. 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.
    3. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
    Full references (including those not matched with items on IDEAS)

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