The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation
In the current study, we investigate the stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the Itô sense. By combining the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-04-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/5/447 |
| _version_ | 1797601101865811968 |
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| author | Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed |
| author_facet | Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed |
| author_sort | Farah M. Al-Askar |
| collection | DOAJ |
| description | In the current study, we investigate the stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the Itô sense. By combining the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion approach with two separate equations, such as the Riccati and elliptic equations, new hyperbolic, trigonometric, rational, and Jacobi elliptic solutions for SBBME-BD can be generated. The solutions to the Benjamin–Bona–Mahony equation are useful in understanding various scientific phenomena, including Rossby waves in spinning fluids and drift waves in plasma. Our results are presented using MATLAB, with numerous 3D and 2D figures illustrating the impacts of white noise and the beta derivative on the obtained solutions of SBBME-BD. |
| first_indexed | 2024-03-11T03:56:44Z |
| format | Article |
| id | doaj.art-756768783cbe43dda20619e8d56fe6b5 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T03:56:44Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-756768783cbe43dda20619e8d56fe6b52023-11-18T00:27:25ZengMDPI AGAxioms2075-16802023-04-0112544710.3390/axioms12050447The Influence of White Noise and the Beta Derivative on the Solutions of the BBM EquationFarah M. Al-Askar0Clemente Cesarano1Wael W. Mohammed2Department of Mathematical Science, Collage of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi ArabiaSection of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyDepartment of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi ArabiaIn the current study, we investigate the stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered stochastic term is the multiplicative noise in the Itô sense. By combining the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">F</mi></semantics></math></inline-formula>-expansion approach with two separate equations, such as the Riccati and elliptic equations, new hyperbolic, trigonometric, rational, and Jacobi elliptic solutions for SBBME-BD can be generated. The solutions to the Benjamin–Bona–Mahony equation are useful in understanding various scientific phenomena, including Rossby waves in spinning fluids and drift waves in plasma. Our results are presented using MATLAB, with numerous 3D and 2D figures illustrating the impacts of white noise and the beta derivative on the obtained solutions of SBBME-BD.https://www.mdpi.com/2075-1680/12/5/447stability by noiseexact solutionsℱ-expansion methodbeta-derivativestochastic BBM |
| spellingShingle | Farah M. Al-Askar Clemente Cesarano Wael W. Mohammed The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation Axioms stability by noise exact solutions ℱ-expansion method beta-derivative stochastic BBM |
| title | The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation |
| title_full | The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation |
| title_fullStr | The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation |
| title_full_unstemmed | The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation |
| title_short | The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation |
| title_sort | influence of white noise and the beta derivative on the solutions of the bbm equation |
| topic | stability by noise exact solutions ℱ-expansion method beta-derivative stochastic BBM |
| url | https://www.mdpi.com/2075-1680/12/5/447 |
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