Operator solutions for fractional Fokker-Planck equations

TL;DR

This paper develops exact solutions for fractional Fokker-Planck equations using evolution operators and Levy stable distributions, exploring various fractional orders, initial conditions, and operator forms.

Contribution

It introduces a novel method employing Levy stable distributions to generate self-reproducing solutions for fractional Fokker-Planck equations.

Findings

Exact solutions for various fractional orders obtained

Explicit cases demonstrate the method's applicability

Solutions adapt to different initial conditions and operators

Abstract

We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.