Analytical insights into solitary wave solutions of the fractional Estevez-Mansfield-Clarkson equation

M. Mossa Al-Sawalha; Saima Noor; Saleh Alshammari; Abdul Hamid Ganie; Ahmad Shafee; M. Mossa Al-Sawalha; Saima Noor; Saleh Alshammari; Abdul Hamid Ganie; Ahmad Shafee

doi:10.3934/math.2024663

AIMS Mathematics

2024, Volume 9, Issue 6: 13589-13606. doi: 10.3934/math.2024663

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Analytical insights into solitary wave solutions of the fractional Estevez-Mansfield-Clarkson equation

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Basic Sciences, Preparatory Year, King Faisal University, Al-Ahsa 31982, Saudi Arabia
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
4.
Basic Science Department, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
5.
PAAET, College of Technological Studies, Laboratory Technology Department, Shuwaikh 70654, Kuwait

Received: 12 January 2024 Revised: 26 March 2024 Accepted: 27 March 2024 Published: 12 April 2024
MSC : 33B15, 34A34, 35A20, 35A22, 44A10

This study delved into the dynamics of wave solutions within the Estevez-Mansfield-Clarkson equation in fractional nonlinear space-time. Utilizing conformable fractional derivatives, the equation governing shallow water phenomena and fluid dynamics was transformed into a nonlinear ordinary differential equation. Applying the Riccati Bernoulli sub-ODE approach yielded a finite series representation. Notably, our findings revealed novel solitary wave solutions characterized by kink, anti-kink, periodic, and shock functions. Visualized through 3D and contour graphs, kink and periodic waves emerged as distinct observable manifestations. Intriguingly, the diversity of results surpassed previous results, contributing to a deeper understanding of the intricate dynamics inherent in the system.
- fractional Estevez-Mansfield-Clarkson (EMC) equation,
- solitary wave solution,
- analytical method
Citation: M. Mossa Al-Sawalha, Saima Noor, Saleh Alshammari, Abdul Hamid Ganie, Ahmad Shafee. Analytical insights into solitary wave solutions of the fractional Estevez-Mansfield-Clarkson equation[J]. AIMS Mathematics, 2024, 9(6): 13589-13606. doi: 10.3934/math.2024663

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Abstract

This study delved into the dynamics of wave solutions within the Estevez-Mansfield-Clarkson equation in fractional nonlinear space-time. Utilizing conformable fractional derivatives, the equation governing shallow water phenomena and fluid dynamics was transformed into a nonlinear ordinary differential equation. Applying the Riccati Bernoulli sub-ODE approach yielded a finite series representation. Notably, our findings revealed novel solitary wave solutions characterized by kink, anti-kink, periodic, and shock functions. Visualized through 3D and contour graphs, kink and periodic waves emerged as distinct observable manifestations. Intriguingly, the diversity of results surpassed previous results, contributing to a deeper understanding of the intricate dynamics inherent in the system.

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