Adomian Decomposition Approach for Solving the Two-Dimensional Fractional Advection-Diffusion Equation

Abstract

This work focuses on improving the modeling of pollutant dispersion in environment where traditional diffusion approaches are inadequate, such as the Kathmandu valley. Motivated by the need for accurate predictions under stagnant atmospheric conditions, especially during winter, this study addresses the limitations of classical models that fail to capture memory effects and slow pollutant spread. A time-fractional advection-diffusion equation (FADE), incorporating fractional derivatives to represent non-classical diffusion is utilized. The Adomian Decomposition Method (ADM) is applied to derive an approximate analytical solution. The results reveal that lower fractional orders depict slower, sub-diffusive transport, whereas higher orders transition toward classical diffusion behavior. This approach effectively models the anomalous dispersion patterns observed in complex terrains, offering an enhanced framework for air quality assessment in situations where traditional methods are inadequate.