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Nonlocal Impulsive Fractional Integral Boundary Value Problem for ( ρ k , ϕ k )-Hilfer Fractional Integro-Differential Equations

Author

Listed:
  • Marisa Kaewsuwan

    (Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

  • Rachanee Phuwapathanapun

    (Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, 06374 Ankara, Türkiye
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    These authors contributed equally to this work.)

  • Jutarat Kongson

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    These authors contributed equally to this work.)

Abstract

In this paper, we establish the existence and stability results for the ( ρ k , ϕ k ) -Hilfer fractional integro-differential equations under instantaneous impulse with non-local multi-point fractional integral boundary conditions. We achieve the formulation of the solution to the ( ρ k , ϕ k ) -Hilfer fractional differential equation with constant coefficients in term of the Mittag–Leffler kernel. The uniqueness result is proved by applying Banach’s fixed point theory with the Mittag–Leffler properties, and the existence result is derived by using a fixed point theorem due to O’Regan. Furthermore, Ulam–Hyers stability and Ulam–Hyers–Rassias stability results are demonstrated via the non-linear functional analysis method. In addition, numerical examples are designed to demonstrate the application of the main results.

Suggested Citation

  • Marisa Kaewsuwan & Rachanee Phuwapathanapun & Weerawat Sudsutad & Jehad Alzabut & Chatthai Thaiprayoon & Jutarat Kongson, 2022. "Nonlocal Impulsive Fractional Integral Boundary Value Problem for ( ρ k , ϕ k )-Hilfer Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(20), pages 1-40, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3874-:d:946462
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    References listed on IDEAS

    as
    1. 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).
    2. Kucche, Kishor D. & Mali, Ashwini D., 2021. "On the nonlinear (k,Ψ)-Hilfer fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Songkran Pleumpreedaporn & Chanidaporn Pleumpreedaporn & Jutarat Kongson & Chatthai Thaiprayoon & Jehad Alzabut & Weerawat Sudsutad, 2022. "Dynamical Analysis of Nutrient-Phytoplankton-Zooplankton Model with Viral Disease in Phytoplankton Species under Atangana-Baleanu-Caputo Derivative," Mathematics, MDPI, vol. 10(9), pages 1-33, May.
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