Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model
This paper studies a fractional biological population model involving the Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition meth...
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University of Maragheh
2024-07-01
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| Series: | Sahand Communications in Mathematical Analysis |
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| Online Access: | https://scma.maragheh.ac.ir/article_711325_f757f6618d054a8b58c62dbea69c6df5.pdf |
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| author | Ali Khalouta |
| author_facet | Ali Khalouta |
| author_sort | Ali Khalouta |
| collection | DOAJ |
| description | This paper studies a fractional biological population model involving the Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition method ($\mathbb{J}$-DM) which is a combined form of the $\mathbb{J}$-transform method and a new decomposition method to solve the proposed model. After the convergence analysis of the $\mathbb{J}$-DM, we provide three numerical examples to illustrate the results obtained. The numerical examples show that this method is easy to use and can give accurate results. |
| format | Article |
| id | doaj-art-1ad8f1329661428ebd2fcfbb060aa4e4 |
| institution | Kabale University |
| issn | 2322-5807 2423-3900 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj-art-1ad8f1329661428ebd2fcfbb060aa4e42025-02-11T05:27:31ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002024-07-0121316519610.22130/scma.2023.2005194.1360711325Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population ModelAli Khalouta0Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas Sétif University 1, 19000 Sétif, Algeria.This paper studies a fractional biological population model involving the Caputo-Fabrizio fractional derivative. We establish the existence and uniqueness of the solution using Banach's fixed point theorem. Furthermore, we propose a new numerical algorithm called $\mathbb{J}$-decomposition method ($\mathbb{J}$-DM) which is a combined form of the $\mathbb{J}$-transform method and a new decomposition method to solve the proposed model. After the convergence analysis of the $\mathbb{J}$-DM, we provide three numerical examples to illustrate the results obtained. The numerical examples show that this method is easy to use and can give accurate results.https://scma.maragheh.ac.ir/article_711325_f757f6618d054a8b58c62dbea69c6df5.pdffractional biological population modelcaputo-fabrizio fractional derivativebanach spacej-transformdecomposition method |
| spellingShingle | Ali Khalouta Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model Sahand Communications in Mathematical Analysis fractional biological population model caputo-fabrizio fractional derivative banach space j-transform decomposition method |
| title | Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model |
| title_full | Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model |
| title_fullStr | Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model |
| title_full_unstemmed | Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model |
| title_short | Existence, Uniqueness and Convergence Solution of Nonlinear Caputo-Fabrizio Fractional Biological Population Model |
| title_sort | existence uniqueness and convergence solution of nonlinear caputo fabrizio fractional biological population model |
| topic | fractional biological population model caputo-fabrizio fractional derivative banach space j-transform decomposition method |
| url | https://scma.maragheh.ac.ir/article_711325_f757f6618d054a8b58c62dbea69c6df5.pdf |
| work_keys_str_mv | AT alikhalouta existenceuniquenessandconvergencesolutionofnonlinearcaputofabriziofractionalbiologicalpopulationmodel |