Computer hardware

Trigonometric functions

Demography

Statistics

Analog signal

Brownian motion

Applied mathematics

Economics

Fractional Brownian motion

Computer science

Digital signal processing

Statistical physics

Signal transfer function

Physics

Mathematics

Geometric Brownian motion

Trigonometry

Diffusion process

Population

Sociology

Mathematical analysis

Geometry

Multiplicative noise

Innovation diffusion

Multiplicative function

Finance

Knowledge management

Fractional calculus

Order (exchange)

Symmetry

Fractional–stochastic Drinfel’d–Sokolov–Wilson equations (FSDSWEs) forced by multiplicative Brownian motion are assumed. This equation is employed in mathematical physics, plasma physics, surface physics, applied sciences, and population dynamics. The (G′/G)-expansion method is utilized to find rational, hyperbolic, and trigonometric stochastic solutions for FSDSWEs. Because of the priority of FSDSWEs, the derived solutions are more useful and effective in understanding various important physical phenomena. Furthermore, we used the MATLAB package to create 3D graphs for specific solutions in order to investigate the effect of fractional-order and Brownian motions on the solutions of FSDSWEs.

The Analytical Solutions of Stochastic-Fractional Drinfel’d-Sokolov-Wilson Equations via (G′/G)-Expansion Method