Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation
Abstract The present study examines the approximate solutions of the time fractional Benjamin Bona Mahony Burger equation. This equation is critical for characterizing the dynamics of water waves and fluid acoustic gravity waves, as well as explaining the unidirectional propagation of long waves in...
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Nature Portfolio
2024-06-01
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| Online Access: | https://doi.org/10.1038/s41598-024-65471-w |
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| author | K. Pavani K. Raghavendar K. Aruna |
| author_facet | K. Pavani K. Raghavendar K. Aruna |
| author_sort | K. Pavani |
| collection | DOAJ |
| description | Abstract The present study examines the approximate solutions of the time fractional Benjamin Bona Mahony Burger equation. This equation is critical for characterizing the dynamics of water waves and fluid acoustic gravity waves, as well as explaining the unidirectional propagation of long waves in nonlinear dispersive systems. This equation also describes cold plasma for hydromagnetic and audio waves in harmonic crystals. The natural transform decomposition method is used to obtain the analytical solution to the time fractional Benjamin Bona Mahony Burger equation. The proposed method uses the Caputo, Caputo Fabrizio, and Atangana Baleanu Caputo derivatives to describe the fractional derivative. We utilize a numerical example with appropriate initial conditions to assess the correctness of our findings. The results of the proposed method are compared to those of the exact solution and various existing techniques, such as the fractional homotopy analysis transform method and the homotopy perturbation transform technique. As a result, bell shaped solitons are discovered under the influence of hyperbolic functions. By comparing the outcomes with tables and graphs, the findings demonstrate the efficacy and effectiveness of the suggested approach. |
| format | Article |
| id | doaj-art-58818bb3d18b4cd8a1ea3ba1289298bf |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-58818bb3d18b4cd8a1ea3ba1289298bf2025-01-26T12:35:14ZengNature PortfolioScientific Reports2045-23222024-06-0114111310.1038/s41598-024-65471-wSolitary wave solutions of the time fractional Benjamin Bona Mahony Burger equationK. Pavani0K. Raghavendar1K. Aruna2Department of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of TechnologyAbstract The present study examines the approximate solutions of the time fractional Benjamin Bona Mahony Burger equation. This equation is critical for characterizing the dynamics of water waves and fluid acoustic gravity waves, as well as explaining the unidirectional propagation of long waves in nonlinear dispersive systems. This equation also describes cold plasma for hydromagnetic and audio waves in harmonic crystals. The natural transform decomposition method is used to obtain the analytical solution to the time fractional Benjamin Bona Mahony Burger equation. The proposed method uses the Caputo, Caputo Fabrizio, and Atangana Baleanu Caputo derivatives to describe the fractional derivative. We utilize a numerical example with appropriate initial conditions to assess the correctness of our findings. The results of the proposed method are compared to those of the exact solution and various existing techniques, such as the fractional homotopy analysis transform method and the homotopy perturbation transform technique. As a result, bell shaped solitons are discovered under the influence of hyperbolic functions. By comparing the outcomes with tables and graphs, the findings demonstrate the efficacy and effectiveness of the suggested approach.https://doi.org/10.1038/s41598-024-65471-wBenjamin Bona Mahony Burger equationAtangana Baleanu Caputo derivativeCaputo Fabrizio derivativeCaputo derivative |
| spellingShingle | K. Pavani K. Raghavendar K. Aruna Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation Scientific Reports Benjamin Bona Mahony Burger equation Atangana Baleanu Caputo derivative Caputo Fabrizio derivative Caputo derivative |
| title | Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation |
| title_full | Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation |
| title_fullStr | Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation |
| title_full_unstemmed | Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation |
| title_short | Solitary wave solutions of the time fractional Benjamin Bona Mahony Burger equation |
| title_sort | solitary wave solutions of the time fractional benjamin bona mahony burger equation |
| topic | Benjamin Bona Mahony Burger equation Atangana Baleanu Caputo derivative Caputo Fabrizio derivative Caputo derivative |
| url | https://doi.org/10.1038/s41598-024-65471-w |
| work_keys_str_mv | AT kpavani solitarywavesolutionsofthetimefractionalbenjaminbonamahonyburgerequation AT kraghavendar solitarywavesolutionsofthetimefractionalbenjaminbonamahonyburgerequation AT karuna solitarywavesolutionsofthetimefractionalbenjaminbonamahonyburgerequation |