Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation
In this article, we analyzed the time fractional higher-dimensional nonlinear modified model of wave propagation, namely the (3 + 1)-dimensional Benjamin–Bona–Mahony-type equation. The fractional sense was defined by the classical Riemann–Liouville fractional derivative. We derived firstly the exist...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/3/124 |
| _version_ | 1797240984604508160 |
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| author | Jian-Gen Liu Yi-Ying Feng |
| author_facet | Jian-Gen Liu Yi-Ying Feng |
| author_sort | Jian-Gen Liu |
| collection | DOAJ |
| description | In this article, we analyzed the time fractional higher-dimensional nonlinear modified model of wave propagation, namely the (3 + 1)-dimensional Benjamin–Bona–Mahony-type equation. The fractional sense was defined by the classical Riemann–Liouville fractional derivative. We derived firstly the existence of symmetry of the time fractional higher-dimensional equation. Next, we constructed the one-dimensional optimal system to the time fractional higher-dimensional nonlinear modified model of wave propagation. Subsequently, it was reduced into the lower-dimensional fractional differential equation. Meanwhile, on the basis of the reduced equation, we obtained its similarity solution. Through a series of analyses of the time fractional high-dimensional model and the results of the above obtained, we can gain a further understanding of its essence. |
| first_indexed | 2024-04-24T18:16:07Z |
| format | Article |
| id | doaj.art-aee955b6dfe241cd8a51bf10380a3fad |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-04-24T18:16:07Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-aee955b6dfe241cd8a51bf10380a3fad2024-03-27T13:42:00ZengMDPI AGFractal and Fractional2504-31102024-02-018312410.3390/fractalfract8030124Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave PropagationJian-Gen Liu0Yi-Ying Feng1School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, ChinaSchool of Mathematics and Statistics, SuZhou University, Suzhou 234000, ChinaIn this article, we analyzed the time fractional higher-dimensional nonlinear modified model of wave propagation, namely the (3 + 1)-dimensional Benjamin–Bona–Mahony-type equation. The fractional sense was defined by the classical Riemann–Liouville fractional derivative. We derived firstly the existence of symmetry of the time fractional higher-dimensional equation. Next, we constructed the one-dimensional optimal system to the time fractional higher-dimensional nonlinear modified model of wave propagation. Subsequently, it was reduced into the lower-dimensional fractional differential equation. Meanwhile, on the basis of the reduced equation, we obtained its similarity solution. Through a series of analyses of the time fractional high-dimensional model and the results of the above obtained, we can gain a further understanding of its essence.https://www.mdpi.com/2504-3110/8/3/124time fractional higher-dimensional nonlinear modified modelsymmetryoptimal systemsimilarity reductionsimilarity solution |
| spellingShingle | Jian-Gen Liu Yi-Ying Feng Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation Fractal and Fractional time fractional higher-dimensional nonlinear modified model symmetry optimal system similarity reduction similarity solution |
| title | Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation |
| title_full | Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation |
| title_fullStr | Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation |
| title_full_unstemmed | Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation |
| title_short | Investigation of the Time Fractional Higher-Dimensional Nonlinear Modified Equation of Wave Propagation |
| title_sort | investigation of the time fractional higher dimensional nonlinear modified equation of wave propagation |
| topic | time fractional higher-dimensional nonlinear modified model symmetry optimal system similarity reduction similarity solution |
| url | https://www.mdpi.com/2504-3110/8/3/124 |
| work_keys_str_mv | AT jiangenliu investigationofthetimefractionalhigherdimensionalnonlinearmodifiedequationofwavepropagation AT yiyingfeng investigationofthetimefractionalhigherdimensionalnonlinearmodifiedequationofwavepropagation |