Abstract
The fractional-stochastic Drinfel’d–Sokolov–Wilson equations (FSDSWEs) perturbed by the multiplicative Wiener process are studied. The mapping method is used to obtain rational, hyperbolic, and elliptic stochastic solutions for FSDSWEs. Due to the importance of FSDSWEs in describing the propagation of shallow water waves, the derived solutions are significantly more useful and effective in understanding various important challenging physical phenomena. In addition, we use the MATLAB Package to generate 3D graphs for specific FSDSWE solutions in order to discuss the impact of fractional order and the Wiener process on the solutions of FSDSWEs.