In this work, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation using conformable derivative. The Riccati method is used to get analytical solutions space-fractional equation. Because has never been examined with and multiplicative noise at same time, generalize some previous results. Moreover, display how influences on stability of obtained

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

In this paper, we study irreducibility of Kuramoto-Sivashinsky equation which is driven by an additive noise acting only on a finite number Fourier modes. order to obtain the irreducibility, first investigate approximate controllability finite-dimensional force, proof based Agrachev-Sarychev type geometric control approach. Next, continuity solving operator for deterministic equation. Finally, ...