@article{Al-Sawalha2024, 
author = {M. Mossa Al-Sawalha and Saima Noor and Saleh Alshammari and Abdul Hamid Ganie and Ahmad Shafee},
title = {Analytical insights into solitary wave solutions of the fractional Estevez-Mansfield-Clarkson equation},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {6},
pages = {13589-13606},
keywords = {fractional Estevez-Mansfield-Clarkson (EMC) equation, solitary wave solution, analytical method},
url = {https://www.sciopen.com/article/10.3934/math.2024663},
doi = {10.3934/math.2024663},
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.}
}