Soliton solutions and fractional effects to the time-fractional modified equal width equation

The one-dimensional long water wave propagation in a nonlinear medium, including the dispersion process, is well simulated by the fractional-order modified equal-width (MEW) equation. This article establishes several recognized, standard, inclusive, and scores of typical exact wave solu-tions to the MEW equation using the (G'/G, 1/G)-expansion method. For specific param-eter values, kink, periodic, periodic-singular, singular-kink, and other forms of solitons can be recovered from general solutions. The effect of the fractional parameter on wave forms has also been analyzed by depicting several graphs for different values of the fractional-order a. In order to illustrate the potential characteristics, three-and two-dimensional combined plots using Maple have been drawn. It has been established that the introduced approach is a potential tool for extracting new exact solutions to various nonlinear evolution equations (NLEEs) arising in engi-neering, science, and applied mathematics. (C) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University .