Existence and Uniqueness of a Fractional Fokker-Planck Equation

TL;DR

This paper proves the existence and uniqueness of weak solutions for a fractional Fokker-Planck equation associated with Levy-driven stochastic differential equations, which model phenomena in geophysical and biochemical sciences.

Contribution

It establishes the mathematical foundation by proving existence and uniqueness of solutions for a nonlocal fractional Fokker-Planck equation.

Findings

Proved existence of weak solutions.

Proved uniqueness of weak solutions.

Applicable to Levy-driven stochastic models.

Abstract

Stochastic differential equations with Levy motion arise the mathematical models for various phenomenon in geophysical and biochemical sciences. The Fokker Planck equation for such a stochastic differential equations is a nonlocal partial differential equations. We prove the existence and uniqueness of the weak solution for this equation.