相关论文: Exact Solutions of the Time Derivative Fokker-Plan…
We propose a probabilistic construction for the solution of a general class of fractional high order heat-type equations in the one-dimensional case, by using a sequence of random walks in the complex plane with a suitable scaling. A time…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered…
We investigate the well-posedness of a coupled Navier-Stokes-Fokker-Planck system with a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of polymeric liquids, where the motion of noninteracting…
We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in…
The fractional Fokker-Planck equation, which contains a variable diffusion coefficient, is discussed and solved. It corresponds to the L\'evy flights in a nonhomogeneous medium. For the case with the linear drift, the solution is stationary…
In this work, we propose adaptive deep learning approaches based on normalizing flows for solving fractional Fokker-Planck equations (FPEs). The solution of a FPE is a probability density function (PDF). Traditional mesh-based methods are…
A general formula in closed form to obtain exact similarity solutions of the Fokker-Planck equation with both time-dependent drift and diffusion coefficients was recently presented by Lin and Ho [ Ann. Phys. \textbf{327}, 386 (2012); J.…
In this article, we propose and study several discrete versions of homogeneous and inhomogeneous one-dimensional Fokker-Planck equations. In particular, for these discretizations of velocity and space, we prove the exponential convergence…
A new method for approximating fractional derivatives of the Gaussian function and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann-Liouville integral using polynomial…
Trapped dynamics widely appears in nature, e.g., the motion of particles in viscous cytoplasm. The famous continuous time random walk (CTRW) model with power law waiting time distribution ({\em having diverging first moment}) describes this…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence $(2-\alpha)$ in time, here $\alpha$ represents the order of the time derivative. The fractional derivative is modeled by…
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…
This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in…
This article presents a finite element scheme with Newton's method for solving the time-fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank-Nicolson scheme based on backward Euler convolution…
The Fokker-Planck equation describes the evolution of the probability density associated with a stochastic differential equation. As the dimension of the system grows, solving this partial differential equation (PDE) using conventional…
A time-fractional Fokker-Planck initial-boundary value problem is considered, with differential operator $u_t-\nabla\cdot(\partial_t^{1-\alpha}\kappa_\alpha\nabla u-\textbf{F}\partial_t^{1-\alpha}u)$, where $0<\alpha <1$. The forcing…