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: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/6648524 |
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| _version_ | 1849398269693657088 |
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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. |
| format | Article |
| id | doaj-art-9d36be7dd0ce420ba1ab015d6a8ce758 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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