A UNIFIED THREE-DIMENSIONAL EXTENDED
FRACTIONAL ANALYTICAL SOLUTION
FOR RADIOACTIVE AIR POLLUTANTS DISPERSION

A novel technique is presented to analytically solve the fractional diffusion equation for non- reactive air pollutants emitted from an elevated continuous source into the air. A generalized methodical solution combining first-order Wentzel–Kramers–Brillouin (WKB) approximation theory and the Sturm–Liouville problem is used to solve the air pollutants’ fractional dispersion equation. Drawing insight from previous analysis, we expanded the initial issue assuming the turbulent flow characteristics appearing in the diffusion process in a non-integer dimensional space. We solved the transformed problem and compared the solutions against data from real experiment. Physical consequences connecting to the conventional generalized diffusion equa- tions are presented. The results indicate that the present solutions are in accordance with thoseobtained in literature. This report demonstrates that fractional equations can be applied in a practical prediction of pollutant dissemination in a turbulent atmosphere.