The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation
Abstract
:1. Introduction
- (1)
- ,
- (2)
- ,
- (3)
- ,
- (4)
- .
2. Traveling Wave Equation for SBBME-BD
3. Exact Solutions of SBBME-BD
3.1. -EM with Riccati Equation
3.2. -EM with Elliptic Equation
Case | P | K | R | |
1 | 1 | |||
2 | 1 | |||
3 | 1 | |||
4 | ||||
5 | ||||
6 | or | |||
7 | ||||
8 | ||||
9 |
4. Impacts of the Beta Derivative and Noise on SBBME-BD Solutions
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Al-Askar, F.M.; Cesarano, C.; Mohammed, W.W. The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation. Axioms 2023, 12, 447. https://doi.org/10.3390/axioms12050447
Al-Askar FM, Cesarano C, Mohammed WW. The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation. Axioms. 2023; 12(5):447. https://doi.org/10.3390/axioms12050447
Chicago/Turabian StyleAl-Askar, Farah M., Clemente Cesarano, and Wael W. Mohammed. 2023. "The Influence of White Noise and the Beta Derivative on the Solutions of the BBM Equation" Axioms 12, no. 5: 447. https://doi.org/10.3390/axioms12050447