Local fractional Fokker-Planck equation

TL;DR

This paper introduces local fractional differential equations and derives a local fractional Fokker-Planck equation, demonstrating its applicability to modeling subdiffusive phenomena in fractal space and time.

Contribution

It presents the first formulation of local fractional Fokker-Planck equations based on recent local fractional derivatives, expanding modeling tools for fractal phenomena.

Findings

Derived a local fractional Fokker-Planck equation from Chapman-Kolmogorov condition.

Solved the equation with specific transition probabilities.

Showed the equation models subdiffusive behavior.

Abstract

New kind of differential equations, called local fractional differential equations, has been proposed for the first time. They involve local fractional derivatives introduced recently. Such equations appear to be suitable to deal with phenomena taking place in fractal space and time. A local fractional analog of Fokker-Planck equation has been derived starting from the Chapman-Kolmogorov condition. Such an equation is solved, with a specific choice of the transition probability, and shown to give rise to subdiffusive behavior.