Exact solutions to the fractional nonlinear phenomena in fluid dynamics via the Riccati-Bernoulli sub-ODE method

Waleed Hamali; Abdulah A. Alghamdi; Waleed Hamali; Abdulah A. Alghamdi

doi:10.3934/math.20241501

AIMS Mathematics

2024, Volume 9, Issue 11: 31142-31162. doi: 10.3934/math.20241501

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Exact solutions to the fractional nonlinear phenomena in fluid dynamics via the Riccati-Bernoulli sub-ODE method

Waleed Hamali ¹,
Abdulah A. Alghamdi ^{2,3
,
,}

1.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, kingdom of Saudi Arabia
2.
Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, kingdom of Saudi Arabia
3.
Center of Modern Mathematical Sciences and their Applications (CMMSA), King Abdulaziz University, Jeddah 21589, kingdom of Saudi Arabia

Received: 03 September 2024 Revised: 17 October 2024 Accepted: 23 October 2024 Published: 01 November 2024
MSC : 34G20, 35A20, 35A22, 35R11

The Riccati-Bernoulli sub-ODE method has been used in recent research to efficiently investigate the analytical solutions of a non-linear equation widely used in fluid dynamics research. By utilizing this method, exact solutions are obtained for the space-time fractional symmetric regularized long-wave equation. These results comprehensively understand the long wave equation widely used in numerous fluid dynamics and wave propagation scenarios. The approach to studying these phenomena and using conceptual representation to understand their essential characteristics opens the door to valuable insights that may help improve both the theoretical and applied aspects of fluid dynamics and similar fields. Thus, as these complex equations demonstrate, the suggested approach is a valuable tool for conducting further research into non-linear phenomena across several disciplines.
Citation: Waleed Hamali, Abdulah A. Alghamdi. Exact solutions to the fractional nonlinear phenomena in fluid dynamics via the Riccati-Bernoulli sub-ODE method[J]. AIMS Mathematics, 2024, 9(11): 31142-31162. doi: 10.3934/math.20241501

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Abstract

The Riccati-Bernoulli sub-ODE method has been used in recent research to efficiently investigate the analytical solutions of a non-linear equation widely used in fluid dynamics research. By utilizing this method, exact solutions are obtained for the space-time fractional symmetric regularized long-wave equation. These results comprehensively understand the long wave equation widely used in numerous fluid dynamics and wave propagation scenarios. The approach to studying these phenomena and using conceptual representation to understand their essential characteristics opens the door to valuable insights that may help improve both the theoretical and applied aspects of fluid dynamics and similar fields. Thus, as these complex equations demonstrate, the suggested approach is a valuable tool for conducting further research into non-linear phenomena across several disciplines.

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