Abstract
This paper presents a numerical method for solving the convection-diffusion equation with a fractional-order Caputo derivative to model air pollution in urban environments. The developed finite element scheme accounts for memory effects, offering a more accurate representation of pollutant transport compared to classical models. Stability and convergence of the method are theoretically proven and supported by numerical experiments. The model effectively identifies pollutant accumulation zones and can forecast air quality under various weather conditions. The results have practical value for improving environmental monitoring systems and planning measures to reduce pollution levels.