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Fractional radial transport in cylindrical geometry

R. Sánchez1,*, D. E. Newman2, and J. A. Mier3

  • *Contact author: raul.sanchez@uc3m.es
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Phys. Rev. E 112, 055205 – Published 13 November, 2025

DOI: https://doi.org/10.1103/w2pz-z9kq

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.

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Phys. Rev. E 112, 055205– Published 13 November, 2025
  • Received 9 August 2025
  • Accepted 20 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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