A transport equation from continuous-time random walk models fractional radial transport, suggesting new approaches to fluid dynamics.
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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>H</a:mi> </a:mrow> </a:math> functions.
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R et al. (2025) studied this question.
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