Application of $$\tan (\phi (\xi )/2)$$ tan ( ϕ ( ξ ) / 2 ) -expansion method for the time-fractional Kuramoto–Sivashinsky equation

Abstract

In this study, with the help of fractional complex transform and new analytical method namely, improved \(\tan (\phi (\xi )/2)\)-expansion method (ITEM), we obtained new solitary wave solution for time-fractional nonlinear Kuramoto–Sivashinsky equation. By using of the fractional complex transform we could convert a nonlinear fractional differential equation into its equivalent ordinary differential equation form. Description of the method is given and the obtained results reveal that the ITEM is a new significant method for exploring nonlinear partial differential models. It is worth mentioning that some of newly obtained solutions are identical to already published results as Tanh method Sahoo and Saha Ray (Phys A 434:240–245, 2015). Therefore, this method can be applied to study many other nonlinear fractional partial differential equations which frequently arise in engineering, mathematical physics and nonlinear optic. Moreover, by using Matlab, some graphical simulations were done to see the behavior of these solutions.