The Exact Solutions of Stochastic Fractional-Space Kuramoto-Sivashinsky Equation by Using (<inline-formula><math display="inline"><semantics><mfrac><msup><mi>G</mi><mo>′</mo></msup><mi>G</mi></mfrac></semantics></math></inline-formula>)-Expansion Method

Abstract

In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the G′G-expansion method. Furthermore, we generalize some previous results that did not use this equation with multiplicative noise and fractional space. Additionally, we show the influence of the stochastic term on the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation.

Keywords

• stochastic Kuramoto–Sivashinsky
• fractional Kuramoto–Sivashinsky
• exact stochastic-fractional solutions
• \({(\frac{G^{\prime }}{G})}\)-expansion method