Dynamical Behavior of the Fractional Coupled Konopelchenko–Dubrovsky and (3 + 1)-Dimensional Modified Korteweg–de Vries–Zakharov–Kuznestsov Equations

This work studies soliton solutions of time-fractional coupled Konopelchenko–Dubrovsky (CKDE) and (3 + 1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznestsov (mKdVZKE) equations. These models are used to define the physical phenomena of ocean dynamics, plasma physics, and soliton theory. The unified method is used to solve these fractional models analytically. To deal with the time fractional part, conformable and local M derivatives are used. A fractional wave transformation is used to transform a fractional partial differential equation to an ordinary differential equation. Using the proposed scheme, soliton solutions are obtained in polynomial and rational forms. The behavior of a soliton solution is also analyzed at different fractional parameters. The results show that the proposed scheme is simple and easy to apply to all types of time-fractional nonlinear homogenous evolution equations encountered in various fields of science.