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

Songkran Pleumpreedaporn, Weerawat Sudsutad, Chatthai Thaiprayoon, Juan E. Nápoles and Jutarat Kongson
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Songkran Pleumpreedaporn: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
Weerawat Sudsutad: Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
Chatthai Thaiprayoon: Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand
Juan E. Nápoles: Facultad de Ciencias Exactas y Naturales y Agrimensura (FaCENA), Universidad Nacional del Nordest (UNNE), Avenue Libertad 5450, Corrientes 3400, Argentina
Jutarat Kongson: Center of Excellence in Mathematics, CHE, Sri Ayutthaya Road, Bangkok 10400, Thailand

Mathematics, 2021, vol. 9, issue 24, 1-31

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.

Keywords: existence and uniqueness; ? -Hilfer fractional derivative; fixed point theorem; Ulam-Hyers stability; nonlinear integral condition; ? -Hilfer Navier problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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