A novel numerical method for solving the Caputo-Fabrizio fractional differential equation
In this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integra...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023481?viewType=HTML |
| _version_ | 1811158429630201856 |
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| author | Sadia Arshad Iram Saleem Ali Akgül Jianfei Huang Yifa Tang Sayed M Eldin |
| author_facet | Sadia Arshad Iram Saleem Ali Akgül Jianfei Huang Yifa Tang Sayed M Eldin |
| author_sort | Sadia Arshad |
| collection | DOAJ |
| description | In this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's 1/3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings. |
| first_indexed | 2024-04-10T05:24:33Z |
| format | Article |
| id | doaj.art-369eeb7711ad4f079c4c710e4391d95d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T05:24:33Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-369eeb7711ad4f079c4c710e4391d95d2023-03-08T01:11:20ZengAIMS PressAIMS Mathematics2473-69882023-02-01849535955610.3934/math.2023481A novel numerical method for solving the Caputo-Fabrizio fractional differential equationSadia Arshad0Iram Saleem 1Ali Akgül 2Jianfei Huang 3Yifa Tang4Sayed M Eldin51. COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan1. COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon 3. Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey 4. Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10, Turkey5. College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China6. LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China7. Center of Research, Faculty of Engineering Future University in Egypt New Cairo 11835, EgyptIn this paper, a unique and novel numerical approach—the fractional-order Caputo-Fabrizio derivative in the Caputo sense—is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's 1/3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.https://www.aimspress.com/article/doi/10.3934/math.2023481?viewType=HTMLfractional differential equationnon-singular operatornumerical approximationstability analysisconvergence analysis |
| spellingShingle | Sadia Arshad Iram Saleem Ali Akgül Jianfei Huang Yifa Tang Sayed M Eldin A novel numerical method for solving the Caputo-Fabrizio fractional differential equation AIMS Mathematics fractional differential equation non-singular operator numerical approximation stability analysis convergence analysis |
| title | A novel numerical method for solving the Caputo-Fabrizio fractional differential equation |
| title_full | A novel numerical method for solving the Caputo-Fabrizio fractional differential equation |
| title_fullStr | A novel numerical method for solving the Caputo-Fabrizio fractional differential equation |
| title_full_unstemmed | A novel numerical method for solving the Caputo-Fabrizio fractional differential equation |
| title_short | A novel numerical method for solving the Caputo-Fabrizio fractional differential equation |
| title_sort | novel numerical method for solving the caputo fabrizio fractional differential equation |
| topic | fractional differential equation non-singular operator numerical approximation stability analysis convergence analysis |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023481?viewType=HTML |
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