New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations
The purpose of this article is to explore a new method for solving one of the nonlinear partial differential equations (NPDE) which is difficult to solve. The dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the solutions of space-time fractional Bateman-Burgers equation is solved by a...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-06-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fams.2025.1568834/full |
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| author | Nathanon Sribua-Iam Settapat Chinviriyasit |
| author_facet | Nathanon Sribua-Iam Settapat Chinviriyasit |
| author_sort | Nathanon Sribua-Iam |
| collection | DOAJ |
| description | The purpose of this article is to explore a new method for solving one of the nonlinear partial differential equations (NPDE) which is difficult to solve. The dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the solutions of space-time fractional Bateman-Burgers equation is solved by a travelling wave analysis method as the Riccati sub-equation. The solutions of space-time fractional DMBBM equation and the solutions of space-time fractional Bateman-Burgers equation can be expressed in the forms of exponential functions, trigonometric functions, rational functions, and hyperbolic functions. The singular wave, singular kink wave, and periodic wave are the representations of the solution graphs. |
| format | Article |
| id | doaj-art-9b9ee7e46437494fbad69dedba43989f |
| institution | OA Journals |
| issn | 2297-4687 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj-art-9b9ee7e46437494fbad69dedba43989f2025-08-20T02:32:06ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872025-06-011110.3389/fams.2025.15688341568834New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equationsNathanon Sribua-IamSettapat ChinviriyasitThe purpose of this article is to explore a new method for solving one of the nonlinear partial differential equations (NPDE) which is difficult to solve. The dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and the solutions of space-time fractional Bateman-Burgers equation is solved by a travelling wave analysis method as the Riccati sub-equation. The solutions of space-time fractional DMBBM equation and the solutions of space-time fractional Bateman-Burgers equation can be expressed in the forms of exponential functions, trigonometric functions, rational functions, and hyperbolic functions. The singular wave, singular kink wave, and periodic wave are the representations of the solution graphs.https://www.frontiersin.org/articles/10.3389/fams.2025.1568834/fulldispersive modified Benjamin-Bona-Mahony (DMBBM) equationBateman-Burgers equationnonlinear partial differential equationtravelling wave analysis methodRiccati sub-equation |
| spellingShingle | Nathanon Sribua-Iam Settapat Chinviriyasit New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations Frontiers in Applied Mathematics and Statistics dispersive modified Benjamin-Bona-Mahony (DMBBM) equation Bateman-Burgers equation nonlinear partial differential equation travelling wave analysis method Riccati sub-equation |
| title | New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations |
| title_full | New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations |
| title_fullStr | New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations |
| title_full_unstemmed | New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations |
| title_short | New analytical wave solutions of fractional order DMBBM and Bateman-Burgers equations |
| title_sort | new analytical wave solutions of fractional order dmbbm and bateman burgers equations |
| topic | dispersive modified Benjamin-Bona-Mahony (DMBBM) equation Bateman-Burgers equation nonlinear partial differential equation travelling wave analysis method Riccati sub-equation |
| url | https://www.frontiersin.org/articles/10.3389/fams.2025.1568834/full |
| work_keys_str_mv | AT nathanonsribuaiam newanalyticalwavesolutionsoffractionalorderdmbbmandbatemanburgersequations AT settapatchinviriyasit newanalyticalwavesolutionsoffractionalorderdmbbmandbatemanburgersequations |