Solving nonlinear evolution equation system using two different methods

Abstract

This paper deals with constructing more general exact solutions of the coupled Higgs equation by using the (G ′ /G, /G)-expansion and ( /G ′ )-expansion methods. The obtained solutions are expressed by three types of functions: hyperbolic, trigonometric and rational functions with free parameters. It has been shown that the suggested methods are productive and will be used to solve nonlinear partial di erential equations in applied mathematics and engineering. Throughout the paper, all the calculations are made with the aid of the Maple software.

Regarding on the exact solutions for the nonlinear fractional differential equations

“…As a result, numerous influential methods have been proposed. Some of these include as the tanh-sech method [6], the (G ′ /G)-expansion method [7], the (G ′ /G, 1/G)-expansion method [8], the first integral method [9], the exponential function method [10,11], the sub equation method [12], the trial equation method [13], ansatz method [14], the modified Kudryashov method [15], variational iteration method [16] and others [17][18][19].…”