Monte Carlo evaluation of FADE approach to anomalous kinetics

TL;DR

This paper compares Monte Carlo simulations of CTRW with fractional derivative models to analyze anomalous diffusion under advection, revising Galilei variant and invariant schemes.

Contribution

It introduces a comparative analysis of CTRW and fractional derivative models for anomalous diffusion, including revised Galilei schemes.

Findings

CTRWs effectively model anomalous diffusion with advection.

Revised schemes improve accuracy of diffusion modeling.

Comparison highlights strengths and limitations of each approach.

Abstract

In this paper we propose a comparison between the CTRW (Monte Carlo) and Fractional Derivative approaches to the modelling of anomalous diffusion phenomena in the presence of an advection field. Galilei variant and invariant schemes are revised.