Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
B.I. Henry (1), T.A.M Langlands (2), P. Straka (1) ((1) Department of, Applied Mathematics, School of Mathematics, Statistics, University of New, South Wales, Sydney, Australia. (2) Department of Mathematics, Computing,, University of Southern Queensland, Toowoomba Queensland
TL;DR
This paper derives a fractional Fokker-Planck equation for subdiffusion influenced by space-and-time-dependent forces, connecting continuous time random walks with stochastic Langevin equations.
Contribution
It introduces a generalized fractional Fokker-Planck equation for subdiffusion under complex force fields, derived from a master equation and linked to Langevin dynamics.
Findings
Derived a new fractional Fokker-Planck equation for subdiffusion.
Established equivalence with a subordinated Langevin equation.
Applicable to general space-and-time-dependent forces.
Abstract
We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.