Abundant soliton solution for the time-fractional stochastic Gray-Scot model under the influence of noise and M-truncated derivative

Abstract

In this study, we investigate the abundant soliton solutions for the time-fractional stochastic Gray-Scot (TFSGS) model analytically. The Gray-Scot model is considered under the influence of M-truncated derivative and multiplicative time noise. This is a reaction–diffusion chemical concentration model that explains the irreversible chemical reaction process. The M-truncated derivative is applied for the fractional version while Brownian motion is taken in the sense of time noise. The novel mathematical technique is used to obtain the abundant families of soliton solutions. These solutions are explored in the form of shock, complicated solitary-shock, shock-singular, and periodic-singular types of single and combination wave structures. During the derivation, the rational solutions also appear. Moreover, we use MATHEMATICA 11.1 tools to plot our solutions and exhibit several three-dimensional, two-dimensional, and their corresponding contour graphs to show the fractional derivative and Brownian motion impact on the soliton solutions of the TFSGS model. We show that the TFDGS model solutions are stabilized at around zero by the multiplicative Brownian motion. These wave solutions represent the chemical concentrations of the reactants.