Abstract
In this article, we consider the stochastic fractional-space long–short-wave interaction system (SFS-LSWIs) forced by multiplicative Brownian motion. To obtain a new exact stochastic fractional-space solutions, we apply two different methods such as sin–cos method and the Riccati–Bernoulli sub-ODE method. These solutions are essential for explaining some difficult and complicated physical phenomena. Because this system has never been investigated using a combination of multiplicative noise and fractional space, we will generalize certain previously obtained results as special cases. Furthermore, we use Matlab to plot 3D surfaces of analytical solutions produced in this study to show the impact of Brownian motion on the analytical solutions of the SFS-LSWIs.
•SFS-LSWIs forced by Brownian motion is considered.•The sine–cosine method and the Riccati–Bernoulli sub-ODE method is applied.•The influence of the Brownian motion on the stability of the analytical solutions.•Using a combination of multiplicative noise and fractional space is the novelity.•We generalized some previous results.