Comprehensive geometric-shaped soliton solutions of the fractional regularized long wave equation in ocean engineering

Abstract

The time-fractional regularized long wave equation is a significant model in the study of ocean engineering, plasma physics, and fluid dynamics. The fractional derivative is contemplated in the beta derivative sense, which is consistent with all the principles of derivative. In this article, the reliable and viable two-variable (G'/G,1/G)-expansion approaches is instigated to generate a variety of novel and generic wave outcomes. Consequently, the presented research provides abundant robust soliton solutions, including periodic soliton, bell-shaped soliton, W-shaped soliton, and some other type solitons. The effect of the fractional-order derivative has also been shown, and it is noticed that the fractional-order derivative has a significant impact on the wave profile. The physical conduct of the solitons has been demonstrated thoroughly via three- and two-dimensional and contour graphs. It can be noted that the new solutions obtained will provide greater convenience in the study of the phenomena described by the regular long-wave equation.