Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation
In this paper, we investigate the fractional damped Burgers' equation using two efficient analytical approaches: the Laplace least squares residual power series method and the Laplace least squares variational iteration method. These techniques integrate the Laplace transform with the least squ...
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| Format: | Article |
| Language: | English |
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AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025324 |
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| author | M. Mossa Al-Sawalha Khalil Hadi Hakami Mohammad Alqudah Qasem M. Tawhari Hussain Gissy |
| author_facet | M. Mossa Al-Sawalha Khalil Hadi Hakami Mohammad Alqudah Qasem M. Tawhari Hussain Gissy |
| author_sort | M. Mossa Al-Sawalha |
| collection | DOAJ |
| description | In this paper, we investigate the fractional damped Burgers' equation using two efficient analytical approaches: the Laplace least squares residual power series method and the Laplace least squares variational iteration method. These techniques integrate the Laplace transform with the least squares residual power series and least squares variational iteration methods, providing highly accurate solutions for nonlinear fractional differential equations. The fractional derivatives are considered in the sense of the Caputo operator, allowing for a more realistic description of physical phenomena with memory effects. Comparative studies with exact and numerical solutions demonstrate the reliability and accuracy of the results. The proposed methodologies provide a powerful framework for solving nonlinear fractional models in fluid dynamics, shock wave theory, and applied sciences. |
| format | Article |
| id | doaj-art-2bbdca09153248c8a8b073b8c7c4c5b7 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2bbdca09153248c8a8b073b8c7c4c5b72025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011037099712610.3934/math.2025324Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equationM. Mossa Al-Sawalha0Khalil Hadi Hakami1Mohammad Alqudah2Qasem M. Tawhari3Hussain Gissy4Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi ArabiaDepartment of Basic Sciences, School of Electrical Engineering & Information Technology, German Jordanian University, Amman 11180, JordanDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi ArabiaDepartment of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi ArabiaIn this paper, we investigate the fractional damped Burgers' equation using two efficient analytical approaches: the Laplace least squares residual power series method and the Laplace least squares variational iteration method. These techniques integrate the Laplace transform with the least squares residual power series and least squares variational iteration methods, providing highly accurate solutions for nonlinear fractional differential equations. The fractional derivatives are considered in the sense of the Caputo operator, allowing for a more realistic description of physical phenomena with memory effects. Comparative studies with exact and numerical solutions demonstrate the reliability and accuracy of the results. The proposed methodologies provide a powerful framework for solving nonlinear fractional models in fluid dynamics, shock wave theory, and applied sciences.https://www.aimspress.com/article/doi/10.3934/math.2025324fractional damped burgers' equationlaplace least squares residual power series methodlaplace least squares variational iteration methodcaputo fractional operators |
| spellingShingle | M. Mossa Al-Sawalha Khalil Hadi Hakami Mohammad Alqudah Qasem M. Tawhari Hussain Gissy Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation AIMS Mathematics fractional damped burgers' equation laplace least squares residual power series method laplace least squares variational iteration method caputo fractional operators |
| title | Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation |
| title_full | Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation |
| title_fullStr | Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation |
| title_full_unstemmed | Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation |
| title_short | Novel Laplace-integrated least square methods for solving the fractional nonlinear damped Burgers' equation |
| title_sort | novel laplace integrated least square methods for solving the fractional nonlinear damped burgers equation |
| topic | fractional damped burgers' equation laplace least squares residual power series method laplace least squares variational iteration method caputo fractional operators |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025324 |
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