Effects of fractional order time derivative on the solitary wave dynamics of the generalized ZK–Burgers equation

Abstract

The generalized ZK-Burgers equation has nonlinear characteristics of the governing equation and helps to understand nonlinear waves in many fluid problems of plasma mediums. This work aims to study the effects of fractional order of derivative on the wave solutions of this interesting equation via exact and analytical approximate solution techniques. The analytical approximate wave solutions are retrieved using homotopy analysis method taking the fractional derivative in Caputo’s sense, while exact solutions are reaped with the help of first integral method taking the fractional derivative in Jumarie’s modified Riemann–Liouville sense. The obtained solutions will be helpful to understand the dynamical framework of many nonlinear physical phenomena.

Keywords

• Wave solutions
• Time-fractional generalized ZK–Burgers equation
• Homotopy analysis method
• First integral method
• Caputo’s derivative
• Jumarie’s modified Riemann–Liouville Derivative