Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
arXiv:1004.4053 · doi:10.1103/PhysRevLett.105.170602
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.
5 pages
References in corpus (3)
Cited by in corpus (43)
- A fractional order recovery SIR model from a stochastic process
- On subdiffusive continuous time random walks with stochastic resetting
- Transmission of Information between Complex Networks: 1/f-Resonance
- Subdiffusive master equation with space dependent anomalous exponent: `Black Swan' effects
- Numerical solution of the time-fractional Fokker-Planck equation with general forcing
- Generalized Elastic Model: Fractional Langevin Description, Fluctuation Relation, and Linear Response
- A fractional Feynman-Kac equation for weak ergodicity breaking
- Fractional advection-diffusion-asymmetry equation
- Semi-Markov approach to continuous time random walk limit processes
- Regularity theory for time-fractional advection-diffusion-reaction equations
- Well-posedness of time-fractional, advection-diffusion-reaction equations
- Time transformation for random walks in the quenched trap model
- Relaxation patterns and semi-Markov dynamics
- Weak subordination breaking for the quenched trap model
- Transport Equations for Subdiffusion with Nonlinear Particle Interaction
- Asymptotic behavior of the solution of the space dependent variable order fractional diffusion equation: ultra-slow anomalous aggregation
- Sub-diffusion in External Potential: Anomalous hiding behind Normal
- Variable Order Fractional Fokker-Planck Equations derived from Continuous Time Random Walks
- Feynman-Kac equation for anomalous processes with space- and time-dependent forces
- Continuous time random walks and Fokker-Planck equation in expanding media
- Nonlinear subdiffusive fractional equations and aggregation phenomenon
- Game theoretic analysis of incomplete markets: emergence of probabilities, nonlinear and fractional Black-Scholes equations
- Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains
- A semidiscrete finite element approximation of a time-fractional Fokker-Planck equation with nonsmooth initial data
- Fokker--Planck and Kolmogorov Backward Equations for Continuous Time Random Walk scaling limits
- Subdiffusive discrete time random walks via Monte Carlo and subordination
- Population heterogeneity in the fractional master equation, ensemble self-reinforcement and strong memory effects
- Analysis of a dilute polymer model with a time-fractional derivative
- Kato classes for Lévy processes
- Analytic solution to space-fractional Fokker-Planck equations for tempered-stable Lévy distributions with spatially linear, time-dependent drift
- Reaction-subdiffusion on moving fluids
- Similarity solutions for a class of Fractional Reaction-Diffusion equation
- Lévy walk dynamics in non-static media
- A Semi-Markov Algorithm for Continuous Time Random Walk Limit Distributions
- Polymer Concentration Regimes from Fractional Microrheology
- A compounded random walk for space-fractional diffusion on finite domains
- Fluid reactive anomalous transport with random waiting time depending on the preceding jump length
- Non-normalizable quasi-equilibrium states under fractional dynamics
- Wasserstein Gradient Flow Formulation of the Time-Fractional Fokker-Planck Equation
- Mathematical modeling and analysis for the chemotactic diffusion in porous media with incompressible Navier-Stokes equations over bounded domain
- Anomalous diffusion and price impact in the fluid-limit of an order book
- Variational time-fractional Mean Field Games
- Uniform stability for a spatially-discrete, subdiffusive Fokker-Planck equation