Construction of new exact solutions to time-fractional two-component evolutionary system of order 2 via different methods

Abstract

This paper is concerned with the applications of five different methods including the sub-equation method, the tanh method, the modified Kudryashov method, the $$\left( \frac{G'}{G}\right)$$ -expansion method and the Exp-function method to construct exact solutions of time-fractional two-component evolutionary system of order 2. We first convert this type of fractional equations to the nonlinear ordinary differential equations by means of fractional complex transform. Then, the five methods are adopted to solve the nonlinear ordinary differential equations. As a result, some new exact solutions are obtained. It is also shown that each of the considered methods can be used as an alternative for solving fractional differential equations.