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( k , ψ )-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions

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)

Abstract

In this paper, we establish existence and uniqueness results for single-valued as well as multi-valued ( k , ψ ) -Hilfer boundary value problems of order in ( 1 , 2 ] , subject to nonlocal integro-multi-point boundary conditions. In the single-valued case, we use Banach and Krasnosel’skiĭ fixed point theorems as well as a Leray–Schauder nonlinear alternative to derive the existence and uniqueness results. For the multi-valued problem, we prove two existence results for the convex and non-convex nature of the multi-valued map involved in a problem by applying a Leray–Schauder nonlinear alternative for multi-valued maps, and a Covitz–Nadler fixed point theorem for multi-valued contractions, respectively. Numerical examples are presented for illustration of all the obtained results.

Suggested Citation

  • Sotiris K. Ntouyas & Bashir Ahmad & Jessada Tariboon, 2022. "( k , ψ )-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2615-:d:872446
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    References listed on IDEAS

    as
    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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    3. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions," Springer Optimization and Its Applications, in: Stochastic Differential Inclusions and Applications, edition 127, chapter 0, pages 147-179, Springer.
    4. 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.
    5. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions and Applications," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-6756-4, December.
    6. Chatterjee, Amar Nath & Ahmad, Bashir, 2021. "A fractional-order differential equation model of COVID-19 infection of epithelial cells," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    7. 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.
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