In this study, a fractional time-space stochastic diffusion equation for modeling pollutant concentration is investigated. The equation is formulated with Caputo fractional derivatives and fractional Laplacians to account for anomalous diffusion processes. Stochastic noise is represented by a combination of Brownian motion and Brownian bridges, simulated using the Karhunen-Loève expansion. The mathematical formulation of the equation is presented, along with initial and boundary conditions. Analytical and numerical methods used to solve the equation are discussed. Results demonstrating the impact of fractional order parameters on pollutant dispersion are provided, offering insights into their physical implications and potential applications in environmental modeling.
