A generalized Gronwall inequality via $ \psi $-Hilfer proportional fractional operators and its applications to nonlocal Cauchy-type system-Reference-Cited by-同舟云学术

A generalized Gronwall inequality via $ \psi $-Hilfer proportional fractional operators and its applications to nonlocal Cauchy-type system

Published:2024 Issue:9 Volume:9 Page:24443-24479
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Sudsutad Weerawat¹,Kongson Jutarat²,Thaiprayoon Chatthai²,Jarasthitikulchai Nantapat³,Kaewsuwan Marisa¹

Affiliation:

1. Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

2. Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

3. Department of General Education, Faculty of Science and Health Technology, Navamindradhiraj University, Bangkok 10300, Thailand

Abstract

<p>This paper establishes a novel generalized Gronwall inequality concerning the $ \psi $-Hilfer proportional fractional operators. Before proving the main results, the solution of the linear nonlocal coupled $ \psi $-Hilfer proportional Cauchy-type system with constant coefficients under the Mittag-Leffler kernel is created. The uniqueness result for the proposed coupled system is established using Banach's contraction mapping principle. Furthermore, a variety of the Mittag-Leffler-Ulam-Hyers stability of the solutions for the proposed coupled system is investigated. Finally, a numerical example is given to show the effectiveness and applicability of the obtained results, and graphical simulations in the case of linear systems are shown.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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