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Nonlocal Integro-Multi-Point ( k , ψ )-Hilfer Type Fractional Boundary Value Problems

Author

Listed:
  • Sotiris K. Ntouyas

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

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • 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)

  • Mohammad S. Alhodaly

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this paper we investigate the criteria for the existence of solutions for single-valued as well as multi-valued boundary value problems involving ( k , ψ ) -Hilfer fractional derivative operator of order in ( 1 , 2 ] , equipped with nonlocal integral multi-point boundary conditions. For the single-valued case, we rely on fixed point theorems due to Banach and Krasnosel’skiĭ, and Leray–Schauder alternative to establish the desired results. The existence results for the multi-valued problem are obtained by applying the Leray–Schauder nonlinear alternative for multi-valued maps for convex-valued case, while the nonconvex-valued case is studied with the aid of Covit–Nadler’s fixed point theorem for multi-valued contractions. Numerical examples are presented for the illustration of the obtained results.

Suggested Citation

  • Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon & Mohammad S. Alhodaly, 2022. "Nonlocal Integro-Multi-Point ( k , ψ )-Hilfer Type Fractional Boundary Value Problems," Mathematics, MDPI, vol. 10(13), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2357-:d:856170
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    References listed on IDEAS

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    1. Kucche, Kishor D. & Mali, Ashwini D., 2021. "On the nonlinear (k,Ψ)-Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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