A comprehensive review of the recent numerical methods for solving FPDEs
Fractional partial differential equations (FPDEs) have gained significant attention in various scientific and engineering fields due to their ability to describe complex phenomena with memory and long-range interactions. Solving FPDEs analytically can be challenging, leading to a growing need for ef...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Walter de Gruyter GmbH
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/119805/ http://psasir.upm.edu.my/id/eprint/119805/1/119805.pdf |
| _version_ | 1848868055563632640 |
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| author | Alsidrani, Fahad Klllçman, Adem Senu, Norazak |
| author_facet | Alsidrani, Fahad Klllçman, Adem Senu, Norazak |
| author_sort | Alsidrani, Fahad |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Fractional partial differential equations (FPDEs) have gained significant attention in various scientific and engineering fields due to their ability to describe complex phenomena with memory and long-range interactions. Solving FPDEs analytically can be challenging, leading to a growing need for efficient numerical methods. This review article presents the recent analytical and numerical methods for solving FPDEs, where the fractional derivatives are assumed in Riemann-Liouville's sense, Caputo's sense, Atangana-Baleanu's sense, and others. The primary objective of this study is to provide an overview of numerical techniques commonly used for FPDEs, focusing on appropriate choices of fractional derivatives and initial conditions. This article also briefly illustrates some FPDEs with exact solutions. It highlights various approaches utilized for solving these equations analytically and numerically, considering different fractional derivative concepts. The presented methods aim to expand the scope of analytical and numerical solutions available for time-FPDEs and improve the accuracy and efficiency of the techniques employed. |
| first_indexed | 2025-11-15T14:46:18Z |
| format | Article |
| id | upm-119805 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:46:18Z |
| publishDate | 2024 |
| publisher | Walter de Gruyter GmbH |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1198052025-09-19T08:00:09Z http://psasir.upm.edu.my/id/eprint/119805/ A comprehensive review of the recent numerical methods for solving FPDEs Alsidrani, Fahad Klllçman, Adem Senu, Norazak Fractional partial differential equations (FPDEs) have gained significant attention in various scientific and engineering fields due to their ability to describe complex phenomena with memory and long-range interactions. Solving FPDEs analytically can be challenging, leading to a growing need for efficient numerical methods. This review article presents the recent analytical and numerical methods for solving FPDEs, where the fractional derivatives are assumed in Riemann-Liouville's sense, Caputo's sense, Atangana-Baleanu's sense, and others. The primary objective of this study is to provide an overview of numerical techniques commonly used for FPDEs, focusing on appropriate choices of fractional derivatives and initial conditions. This article also briefly illustrates some FPDEs with exact solutions. It highlights various approaches utilized for solving these equations analytically and numerically, considering different fractional derivative concepts. The presented methods aim to expand the scope of analytical and numerical solutions available for time-FPDEs and improve the accuracy and efficiency of the techniques employed. Walter de Gruyter GmbH 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/119805/1/119805.pdf Alsidrani, Fahad and Klllçman, Adem and Senu, Norazak (2024) A comprehensive review of the recent numerical methods for solving FPDEs. Open Mathematics, 22 (1). art. no. 20240036. pp. 1-27. ISSN eISSN: 2391-5455 https://www.degruyterbrill.com:443/document/doi/10.1515/math-2024-0036/html 10.1515/math-2024-0036 |
| spellingShingle | Alsidrani, Fahad Klllçman, Adem Senu, Norazak A comprehensive review of the recent numerical methods for solving FPDEs |
| title | A comprehensive review of the recent numerical methods for solving FPDEs |
| title_full | A comprehensive review of the recent numerical methods for solving FPDEs |
| title_fullStr | A comprehensive review of the recent numerical methods for solving FPDEs |
| title_full_unstemmed | A comprehensive review of the recent numerical methods for solving FPDEs |
| title_short | A comprehensive review of the recent numerical methods for solving FPDEs |
| title_sort | comprehensive review of the recent numerical methods for solving fpdes |
| url | http://psasir.upm.edu.my/id/eprint/119805/ http://psasir.upm.edu.my/id/eprint/119805/ http://psasir.upm.edu.my/id/eprint/119805/ http://psasir.upm.edu.my/id/eprint/119805/1/119805.pdf |