An analytical approach to the solution of fractional-coupled modified equal width and fractional-coupled Burgers equations

Abstract

We opted to construct a traveling wave solution to the nonlinear space-time fractional coupled modified equal width (CMEW) equation and the space-time fractional-coupled Burgers equation, which are often used as an electro-hydro-dynamical model to advance the local electric field and particle acoustic waves in plasma, the shallow water wave issues and portray the variety additional time of an actual structure on the partial liquid mechanics framework, particle acoustic waves through a gas-filled line, and certain consistent state gooey liquid. In this study, we employ the two variable (G′/G,1/G)-expansion method to create further general solitary wave solutions to those equations based on Riemann– Liouville fractional derivative. The fractional differential wave transform simplifies by generating ordinary differential equations (ODE) from fractional-order differential equations. We identified multiple types of solutions through the maple that are illustrated using 3D shape, 3D list point plot, and contour narratives. Additionally, we proposed that the methodology be changed to be more pragmatic, economical, and dependable and that we investigate more generalized precise solutions for traveling waves, such as solitary wave solutions.