Dynamic behaviour and semi-analytical solution of nonlinear fractional-order Kuramoto–Sivashinsky equation

In this paper, we apply the fractional homotopy perturbation transform method (FHPTM) to deliver an effective semi-analytical technique for determining fractional-order Kuramoto–Sivashinsky equations. The project technique combines the Laplace transform with the Caputo–Fabrizio fractional derivative of order \(\alpha \) $\alpha$ where \(\alpha \in (0, 1]\) $\alpha \in (0,1]$ . Fractional-order Kuramoto–Sivashinsky equation is indeed important in the field of nonlinear physics and mathematics. It is a fractional partial differential equation that describes the behaviour of waves in certain dissipative media, such as flames and chemicals. The FHPTM is described to be fast and accurate.  Illustrative examples are included to demonstrate the efficiency and reliability of the presented techniques.