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

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 propos...

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Main Authors: Abdellatif Ben Makhlouf, Mondher Benjemaa, Djalal Boucenna, Lassaad Mchiri, Mohamed Rhaima
Format: Article
Language:English
Published: Wiley 2023-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2023/6648524
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author Abdellatif Ben Makhlouf
Mondher Benjemaa
Djalal Boucenna
Lassaad Mchiri
Mohamed Rhaima
author_facet Abdellatif Ben Makhlouf
Mondher Benjemaa
Djalal Boucenna
Lassaad Mchiri
Mohamed Rhaima
author_sort Abdellatif Ben Makhlouf
collection DOAJ
description 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.
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institution Kabale University
issn 1607-887X
language English
publishDate 2023-01-01
publisher Wiley
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series Discrete Dynamics in Nature and Society
spelling doaj-art-9d36be7dd0ce420ba1ab015d6a8ce7582025-08-20T03:38:39ZengWileyDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/6648524On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential EquationsAbdellatif Ben Makhlouf0Mondher Benjemaa1Djalal Boucenna2Lassaad Mchiri3Mohamed Rhaima4Department of MathematicsDepartment of MathematicsLaboratory of Physical Chemistry and Biology of MaterialsENSIIEDepartment of Statistics and Operations ResearchThe 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.http://dx.doi.org/10.1155/2023/6648524
spellingShingle Abdellatif Ben Makhlouf
Mondher Benjemaa
Djalal Boucenna
Lassaad Mchiri
Mohamed Rhaima
On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
Discrete Dynamics in Nature and Society
title On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
title_full On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
title_fullStr On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
title_full_unstemmed On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
title_short On Generalized Proportional Fractional Order Derivatives and Darboux Problem for Partial Differential Equations
title_sort on generalized proportional fractional order derivatives and darboux problem for partial differential equations
url http://dx.doi.org/10.1155/2023/6648524
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