Abundant Exact Solutions of the Fractional Stochastic Bogoyavlenskii Equation

Abstract

The stochastic Bogoyavlenskii equation with M‐truncated derivatives (SBE‐MTD) is considered in this article. Our objective in this paper is to find the exact solutions to this problem by using the (G′/G)‐expansion and Jacobi elliptic function methods. Due to the fact that this equation is used in fluid dynamics, plasma physics, and nonlinear optics, the acquired results here will aid researchers in characterizing a vast array of intriguing physical phenomena. By providing several graphical representations, we examine how the stochastic term and M‐truncated derivative affect the dynamics of the acquired solutions. Finally, we conclude that the Wiener process stabilizes the solutions of the Bogoyavlenskii equation, and the M‐truncated derivatives shift the surface to the left as the derivative’s order decreases.