Fractional radial transport in cylindrical geometry

Abstract

A transport equation is derived from microscopic considerations, aimed at modeling fractional radial transport in cylindrical-like geometries. The procedure generalizes existing work on one-dimensional Cartesian systems. The transport equation emerges as the fluid limit of an underlying continuous-time random walk (CTRW) that preserves the required symmetries and conservation laws. In the process, appropriate radial fractional operators are identified and defined through their Hankel transforms, providing a smooth interpolation between standard radial differential operators. Finally, propagators for the radial fractional transport equation are obtained in terms of Fox H functions.