Closed-form travelling wave solutions to the nonlinear space-time fractional coupled Burgers’ equation

Abstract

Fractional order nonlinear evolution equations play important roles to give a depiction of the complex physical phenomena of real world. The main aim of this article is to extract exact analytic solutions to the space-time fractional coupled Burgers’ equation in the sense of conformable fractional derivative. A suitable composite transformation is implemented to reduce the considered equation into an ordinary differential equation of fractional order. Then a new approach, called the rational fractional -expansion method, the Exp-function method and the extended tanh method, is employed to construct the closed-form solutions. This effort makes available the travelling wave solutions in terms of hyperbolic function, trigonometric function and rational function, which are found to be newer and more general than the existing results in the literature. The proposed method is highly efficient and may further be used to invstigate entirely new solutions to many other fractional evolution equations.

Keywords

• the rational fractional -expansion method
• the exp-function method
• the extended tanh method
• nonlinear fractional pdes
• conformable fractional derivative
• composite transformation