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Integro-Differential Boundary Conditions to the Sequential ψ 1 -Hilfer and ψ 2 -Caputo Fractional Differential Equations

Author

Listed:
  • Surang Sitho

    (Department of Social and Applied Science, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece)

  • Chayapat Sudprasert

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

Abstract

In this paper, we introduce and study a new class of boundary value problems, consisting of a mixed-type ψ 1 -Hilfer and ψ 2 -Caputo fractional order differential equation supplemented with integro-differential nonlocal boundary conditions. The uniqueness of solutions is achieved via the Banach contraction principle, while the existence of results is established by using the Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating the obtained results.

Suggested Citation

  • Surang Sitho & Sotiris K. Ntouyas & Chayapat Sudprasert & Jessada Tariboon, 2023. "Integro-Differential Boundary Conditions to the Sequential ψ 1 -Hilfer and ψ 2 -Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:867-:d:1061902
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    References listed on IDEAS

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    1. Chanakarn Kiataramkul & Sotiris K. Ntouyas & Jessada Tariboon, 2021. "Existence Results for - Hilfer Fractional Integro-Differential Hybrid Boundary Value Problems for Differential Equations and Inclusions," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-12, September.
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