The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative

Abstract

Fractional order models involving nonlinearity are remarkable for having substantial application in real-world. The present determination is due to obtain applicable wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise. Enhanced rational (G′/G)-expansion and improved auxiliary equation approaches are imposed to the suggested model which accumulate diverse wave solutions in appropriate form. The investigators might depict sophisticated tangible phenomena in a wide range with the assistance of the found well-furnished wave solutions as the governing equation makes understanding about the plasma physics, the wave of propulsion fluid-flow, and the dynamic characteristics of shallow-water waves. Various obtained solutions are figured out to portray prominent physical characteristics of nonlinear wave outlines. Different types of solitons are organized graphically in 3D shapes such as periodic, anti-periodic, compacton, anti-compacton, bell, anti-bell, peakon, kink, anti-kink, cuspon etc. Diverse 2D plots are comprised to make noticeable the wave velocity while contour plots signify the association among the concerned variables. The graphical representations are brought out together with the effects of noise strength and Brownian motion. The observation of the current whole work might captivate the researchers for future related work by employing the recommended approaches which are competent, pioneering, and concise.