Impact of Brownian Motion on the Analytical Solutions of the Space-Fractional Stochastic Approximate Long Water Wave Equation

Abstract

The space-fractional stochastic approximate long water wave equation (SFSALWWE) is considered in this work. The Riccati equation method is used to get analytical solutions of the SFSALWWE. This equation has never been examined with stochastic term and fractional space at the same time. In general, the noise term that preserves the symmetry reduces the domain of instability. To check the impact of Brownian motion on these solutions, we use a MATLAB package to plot 3D and 2D graphs for some analytical fractional stochastic solutions.