Stochastic Solution of Fractional Fokker-Planck Equations with Space-Time-Dependent Coefficients

TL;DR

This paper presents a comprehensive stochastic approach to solving fractional Fokker-Planck equations with space-time-dependent coefficients, extending previous results to more general subdiffusive systems driven by Lévy processes.

Contribution

It introduces a general stochastic solution framework for fractional Fokker-Planck equations with variable coefficients, expanding the scope of prior models.

Findings

Derived explicit stochastic representations for subdiffusion equations.

Extended existing models to include space-time-dependent coefficients.

Validated solutions through theoretical analysis.

Abstract

This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and jump coefficients, thus significantly extends Magdziarz and Zorawik's result in "M. Magdziarz and T. Zorawik, Stochastic representation of fractional subdiffusion equation. The case of infinitely divisible waiting times, L\'evy noise and space-time-dependent coefficients. Proc. Amer. Math. Soc., Accepted (2015)." Fractional Fokker-Planck equation describing subdiffusion is solved by our result in full generality from perspective of stochastic representation.