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Updated: Nov 27, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Non-Linear Langevin and Fractional Fokker-Planck Equations for Anomalous Diffusion by Lévy Stable Processes
Johan Anderson1, Sara Moradi2, Tariq Rafiq3
1Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Göteborg, Sweden.
Abstract:
The numerical solutions to a non-linear Fractional Fokker-Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.
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