On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations-Reference-Cited by-同舟云学术

On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations

Published:2023-08-19 Issue: Volume:2023 Page:1-22
ISSN:1607-887X
Container-title:Discrete Dynamics in Nature and Society
language:en
Short-container-title:Discrete Dynamics in Nature and Society

Author:

Ben Makhlouf Abdellatif¹^ORCID,Benjemaa Mondher¹^ORCID,Boucenna Djalal²^ORCID,Mchiri Lassaad³^ORCID,Rhaima Mohamed⁴^ORCID

Affiliation:

1. Department of Mathematics, Faculty of Sciences of Sfax, Sfax University, Sfax, Tunisia

2. Laboratory of Physical Chemistry and Biology of Materials, Higher Normal School of Technological Education (ENSET), Skikda 21000, Algeria

3. ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes Cedex, France

4. Department of Statistics and Operations Research, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract

The study of the existence and uniqueness of solutions to 2D systems utilizing the generalized proportional fractional derivative operator is the focus of this work. We also derive a finite difference scheme in order to numerically approximate such an operator, and we prove that the method we propose is convergent. Several tests are performed at the end to illustrate the robustness of our algorithm.

Funder

King Saud University

Publisher

Hindawi Limited

Subject

Modeling and Simulation

Link

http://downloads.hindawi.com/journals/ddns/2023/6648524.pdf

Reference22 articles.

1. An adaptive central difference Kalman filter approach for state of charge estimation by fractional order model of lithium-ion battery

2. Chaotic Oscillations in a Fractional-Order Circuit with a Josephson Junction Resonator and Its Synchronization Using Fuzzy Sliding Mode Control

3. A fractional viscoelastic model for laminated glass sandwich plates under blast actions

4. A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms

5. Some results for a class of two-dimensional fractional hyperbolic differential systems with time delay

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