The Influence of Noise on the Solutions of Fractional Stochastic Bogoyavlenskii Equation

We look at the stochastic fractional-space Bogoyavlenskii equation in the Stratonovich sense, which is driven by multiplicative noise. Our aim is to acquire analytical fractional stochastic solutions to this stochastic fractional-space Bogoyavlenskii equation via two different methods such as the exp(−Φ(η))-expansion method and sine–cosine method. Since this equation is used to explain the hydrodynamic model of shallow-water waves, the wave of leading fluid flow, and plasma physics, scientists will be able to characterize a wide variety of fascinating physical phenomena with these solutions. Furthermore, we evaluate the influence of noise on the behavior of the acquired solutions using 2D and 3D graphical representations.