Abstract
In this paper, we consider the fractional-stochastic Boussinesq-Burger system (FSBBS) generated by the multiplicative Brownian motion. The Jacobi elliptic function techniques are used to create creative elliptic, hyperbolic, and rational fractional-stochastic solutions for FSBBS. Furthermore, we draw 2D and 3D graphs by using the MATLAB Package for some obtained solutions of FSBBS to discuss the influence of the Brownian motion on these solutions. Finally, we indicate that the Brownian motion stabilizes the solutions of FSBBS around zero.