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Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function

Author

Listed:
  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece)

  • Phollakrit Wongsantisuk

    (Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Ayub Samadi

    (Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran)

  • 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, a new class of coupled hybrid systems of proportional sequential ψ -Hilfer fractional differential equations, subjected to nonlocal boundary conditions were investigated. Based on a generalization of the Krasnosel’ski i ˘ ’s fixed point theorem due to Burton, sufficient conditions were established for the existence of solutions. A numerical example was constructed illustrating the main theoretical result. For special cases of the parameters involved in the system many new results were covered. The obtained result is new and significantly contributes to existing results in the literature on coupled systems of proportional sequential ψ -Hilfer fractional differential equations.

Suggested Citation

  • Sotiris K. Ntouyas & Phollakrit Wongsantisuk & Ayub Samadi & Jessada Tariboon, 2024. "Hybrid System of Proportional Hilfer-Type Fractional Differential Equations and Nonlocal Conditions with Respect to Another Function," Mathematics, MDPI, vol. 12(7), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:1071-:d:1369092
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    References listed on IDEAS

    as
    1. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
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