Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation

Abstract

A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker–Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality ( α ) of the stable Lévy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index α is computed.