Langevin Approach to Fractional Diffusion Equations including Inertial Effects

TL;DR

This paper explores fractional diffusion equations with inertial effects, linking them to Langevin equations through subordination, advancing the understanding of anomalous diffusion processes.

Contribution

It introduces a novel connection between fractional diffusion equations and Langevin dynamics incorporating inertial effects using subordination.

Findings

Established a relationship between fractional equations and Langevin models.

Demonstrated the role of subordination in deriving fractional diffusion equations.

Extended the Langevin approach to include inertial effects in fractional diffusion.

Abstract

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H.C. Fogedby, Phys. Rev. E {\bf 50}, 041103 (1994), we show how these equations are related to Langevin equations via the procedure of subordination.