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On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions

Author

Listed:
  • Muath Awadalla

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia)

  • Kinda Abuasbeh

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia)

  • Muthaiah Subramanian

    (Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641020, India)

  • Murugesan Manigandan

    (Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore 641020, India)

Abstract

In this article, we investigate sufficient conditions for the existence and stability of solutions to a coupled system of ψ -Caputo hybrid fractional derivatives of order 1 < υ ≤ 2 subjected to Dirichlet boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of the Leray–Schauder alternative theorem and Banach’s contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam–Hyers. Finally, we provide one example in order to show the validity of our results.

Suggested Citation

  • Muath Awadalla & Kinda Abuasbeh & Muthaiah Subramanian & Murugesan Manigandan, 2022. "On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions," Mathematics, MDPI, vol. 10(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1681-:d:815233
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    References listed on IDEAS

    as
    1. Singh, Jagdev & Jassim, Hassan Kamil & Kumar, Devendra, 2020. "An efficient computational technique for local fractional Fokker Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    2. Ricardo Almeida, 2017. "Variational Problems Involving a Caputo-Type Fractional Derivative," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 276-294, July.
    3. Surang Sitho & Sotiris K. Ntouyas & Ayub Samadi & Jessada Tariboon, 2021. "Boundary Value Problems for ψ -Hilfer Type Sequential Fractional Differential Equations and Inclusions with Integral Multi-Point Boundary Conditions," Mathematics, MDPI, vol. 9(9), pages 1-18, April.
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