New approach to find exact solutions of time-fractional Kuramoto–Sivashinsky equation

• New novel method has been proposed.
• The proposed method is well suited for fractional Kuramoto–Sivashinsky equation.
• The performance of this method is reliable.
• This method provides the exact travelling wave solutions.
• Fractional Kuramoto–Sivashinsky equation has been first time solved by this method.

In the present paper, we construct the analytical exact solutions of a nonlinear evolution equation in mathematical physics, viz. time-fractional Kuramoto–Sivashinsky equation by a new proposed method via fractional complex transform. As a result, new types of exact analytical solutions are obtained. Here the fractional derivative is described in Jumarie’s modified Riemann–Liouville sense.