Fractional radial transport in cylindrical geometry.

Area of Science:

• Physics
• Applied Mathematics
• Transport Phenomena

Background:

• Modeling particle transport in complex geometries is crucial for various scientific fields.
• Existing models often simplify geometries, limiting their applicability.
• Fractional calculus offers advanced tools for describing anomalous transport phenomena.

Purpose of the Study:

• To derive a novel transport equation for fractional radial transport in cylindrical-like geometries.
• To generalize existing one-dimensional Cartesian transport models.
• To provide a robust mathematical framework for anomalous diffusion in radial systems.

Main Methods:

• Derivation of the transport equation from microscopic considerations.
• Utilizing the fluid limit of a continuous-time random walk (CTRW).
• Identification and definition of radial fractional operators via Hankel transforms.

Main Results:

• A generalized fractional radial transport equation applicable to cylindrical geometries.
• The CTRM framework ensures preservation of essential symmetries and conservation laws.
• Radial fractional operators are defined, interpolating between standard differential operators.

Conclusions:

• The derived equation offers a more accurate description of fractional radial transport.
• The method provides a unified approach for modeling anomalous transport.
• The use of Fox H functions simplifies the analysis of propagators for the new equation.