Analytical solution of the steady-state atmospheric fractional diffusion equation in a finite domain

In this work, an analytical solution for the steady-state fractional advection-diffusion equation was investigated to simulate the dispersion of air pollutants in a finite media. The authors propose a method that uses classic integral transform technique (CITT) to solve the transformed problem with a fractional derivative, resulting in a more general solution. We compare the solutions with data from real experiment. Physical consequences are discussed with the connections to generalised diffusion equations. In the wake of these analysis, the results indicate that the present solutions are in good agreement with those obtained in the literature. This report demonstrates that fractional equations have come of age as a decisive tool to describe anomalous transport processes.

Automated summary

The authors investigated an analytical solution for the steady-state fractional advection-diffusion equation to simulate air pollutants dispersion in a finite media. They proposed a method using classic integral transform technique (CITT) to solve the transformed problem with a fractional derivative, and compared the solutions with experimental data, demonstrating good agreement with literature results. This study indicates that fractional equations have become a mature tool for describing anomalous transport processes.