Related papers: Fokker-Planck Equation with Fractional Coordinate …
A covariant Fokker-Planck type equation for a simple gas and an equation for the Brownian motion are derived from a relativistic kinetic theory based on the Boltzmann equation. For the simple gas the dynamic friction four-vector and the…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of Fontbona-Gu\'erin-M\'el\'eard, we propose a…
The Fokker-Planck equation is a partial differential equation which is a key ingredient in many models in physics. This paper aims to obtain a quantum counterpart of Fokker-Planck dynamics, as a means to describing quantum Fokker-Planck…
By replacing the spatial derivative with the Dunkl derivative, we generalize the Fokker-Planck equation in (1+1) dimensions. We obtain the Dunkl-Fokker-Planck eigenvalues equation and solve it for the harmonic oscillator plus a…
The Fokker-Planck equation can be reformulated as a continuity equation, which naturally suggests using the associated velocity field in particle flow methods. While the resulting probability flow ODE offers appealing properties - such as…
Extended systems governed by partial differential equations can, under suitable conditions, be approximated by means of sets of ordinary differential equations for global quantities capturing the essential features of the systems dynamics.…
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…
The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional…
The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional…
We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the…
The Fokker_Planck equation can be derived in a consistent manner through a microscopic approach based on a unified scheme of classical and quantum mechanics. Here we shall derive it through a purely quantum mechanical approach based on the…
We consider the kinetic Fokker-Planck equation with a class of general force. We prove the existence and uniqueness of a positive normalized equilibrium (in the case of a general force) and establish some exponential rate of convergence to…
Starting from a forward--backward path integral of a point particle in a bath of harmonic oscillators, we derive the Fokker-Planck and Langevin equations with and without inertia. Special emphasis is placed upon the correct operator order…
In this work, we investigate a variational formulation for a time-fractional Fokker-Planck equation which arises in the study of complex physical systems involving anomalously slow diffusion. The model involves a fractional-order Caputo…
A variational principle is developed for fractional kinetics based on the auxiliary-field formalism. It is applied to the Fokker-Planck equation with spatio-temporal fractionality, and a variational solution is obtained with the help of the…
We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…
By using similarity transformations approach, the exact propagator for a generalized one-dimensional Fokker-Planck equation, with linear drift force and space-time dependent diffusion coefficient, is obtained. The method is simple and…