( G ′/ G , 1/ G )‐Expansion Method

Abstract

This chapter employs the ( G ′/ G , 1/ G )-expansion method to find the exact traveling wave solutions of nonlinear fractional partial differential equation (PDE) defined in the modified Riemann–Liouville sense. In this method, a nonlinear fractional complex transformation turns the fractional PDE into a nonlinear ordinary differential equation of integer order. A system of nonlinear algebraic equations is generated from the fractional PDE when the approach is applied. In order to illustrate the usefulness of this method, the nonlinear time-fractional classical Burgers equation has been solved using this approach. The obtained solutions are expressed in hyperbolic, trigonometric, and rational function solutions. This approach can be considered as an extension of the well-known ( G ′/ G )-expansion method. The two variable ( G ′/ G , 1/ G )-expansion approach is demonstrated to be a more powerful mathematical tool than ( G ′/ G ) and ( G ′/ G 2 )-expansion method for solving nonlinear fractional PDEs in mathematical physics.