Abstract
•To investigate the modified equal width nonlinear space–time variable-order fractional differential equation.•To reduce the variable-order differential equation into an ordinary differential equation using transformation.•To implement modified (G'/G) -expansion method to constructnew travelling wave solutions.•To illustrate the simulation for one-dimensional wave transmission in nonlinear media with dispersion processes.•Applications of modified (G'/G) -expansion in various fields of physical sciences and engineering.
The variable-order evolution equation is an impressive mathematical model that explain complex dynamical problems efficiently and accurately. This latest research investigates the modified equal width nonlinear space–time variable-order fractional differential equation and fractional derivative operator in the sense of Caputo. Using transformation, an ordinary differential equation is obtained from the variable-order differential equation. For accuracy, the space–time variable-order fractional modified equal width equation is solved by the modified (G'/G) -expansion method. This model describes the simulation for one-dimensional wave transmission in nonlinear media with dispersion processes. As a result, new traveling wave solutions are developed for various values of parameters. The obtained solutions have several applications in a recent area of research in mathematical physics. The obtained graphical solutions are in the form of singular solitons, kink solitons and periodic solitons waves which demonstrate that the physical signifance and dynamical behaviors of fractional variable-order differential equations and the proposed method are more effective, powerful, and easy in solving problems arising in mathematical physics.