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A Study of ψ -Hilfer Fractional Boundary Value Problem via Nonlinear Integral Conditions Describing Navier Model

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  • Songkran Pleumpreedaporn

    (Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    These authors contributed equally to this work.)

  • Juan E. Nápoles

    (Facultad de Ciencias Exactas y Naturales y Agrimensura (FaCENA), Universidad Nacional del Nordest (UNNE), Avenue Libertad 5450, Corrientes 3400, Argentina
    Facultad Regional Resistencia (FRRE), Universidad Tecnológica Nacional (UTN), French 414, Resistencia, Chaco 3500, Argentina
    These authors contributed equally to this work.)

  • Jutarat Kongson

    (Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
    Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    These authors contributed equally to this work.)

Abstract

This paper investigates existence, uniqueness, and Ulam’s stability results for a nonlinear implicit ψ -Hilfer FBVP describing Navier model with NIBC s. By Banach’s fixed point theorem, the unique property is established. Meanwhile, existence results are proved by using the fixed point theory of Leray-Schauder’s and Krasnoselskii’s types. In addition, Ulam’s stability results are analyzed. Furthermore, several instances are provided to demonstrate the efficacy of the main results.

Suggested Citation

  • Songkran Pleumpreedaporn & Weerawat Sudsutad & Chatthai Thaiprayoon & Juan E. Nápoles & Jutarat Kongson, 2021. "A Study of ψ -Hilfer Fractional Boundary Value Problem via Nonlinear Integral Conditions Describing Navier Model," Mathematics, MDPI, vol. 9(24), pages 1-31, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3292-:d:705259
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    References listed on IDEAS

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    1. Sarita Nandal & Mahmoud A. Zaky & Rob H. De Staelen & Ahmed S. Hendy, 2021. "Numerical Simulation for a Multidimensional Fourth-Order Nonlinear Fractional Subdiffusion Model with Time Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
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