Results 41 to 50 of about 73,120 (246)
Derivation of the Fractional Fokker–Planck Equation for Stable Lévy with Financial Applications
Mathematics, 2023 This paper aims to propose a generalized fractional Fokker–Planck equation based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion.
Reem Abdullah Aljethi, Adem Kılıçman
doaj +1 more source
Propagation of chaos for the Vlasov–Poisson–Fokker–Planck equation with a polynomial cut-off [PDF]
Communications in Contemporary Mathematics, 2018 We consider a [Formula: see text]-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity.
J. Carrillo, Young-Pil Choi, Samir Salem
semanticscholar +1 more source
Local Fractional Fokker-Planck Equation [PDF]
Physical Review Letters, 1998 New kind of differential equations, called local fractional differential equations, has been proposed for the first time. They involve local fractional derivatives introduced recently. Such equations appear to be suitable to deal with phenomena taking place in fractal space and time.
Kolwankar, Kiran M., Gangal, Anil D.
openaire +3 more sources
A fractional model to describe the Brownian motion of particles and its analytical solution
Advances in Mechanical Engineering, 2015 In this article, we apply a relatively modified analytic iterative method for solving a time-fractional Fokker–Planck equation subject to given constraints.
Jing-Jing Yao, Amit Kumar, Sunil Kumar
doaj +1 more source
Stochastic nonlinear Fokker–Planck equations [PDF]
Nonlinear Analysis, 2019 The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with common noise. The uniqueness of solutions is obtained without any higher moment assumption on the solution by means of ...
Coghi M., Gess B.
openaire +6 more sources
Fokker-Planck Equation and Thermodynamic System Analysis
Entropy, 2015 The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann’s definition of entropy ...
Umberto Lucia, Gianpiero Gervino
doaj +1 more source
, 2007 The purpose of this comment is to correct mistaken assumptions and claims made in the paper Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations by T. D. Frank.
Arnold +12 more
core +1 more source
Fokker–Planck equation on fractal curves [PDF]
Chaos, Solitons & Fractals, 2013 A Fokker Planck equation on fractal curves is obtained, starting from Chapmann-Kolmogorov equation on fractal curves. This is done using the recently developed calculus on fractals, which allows one to write differential equations on fractal curves. As an important special case, the diffusion and drift coefficients are obtained, for suitable transition
Satin, Seema E. +2 more
openaire +3 more sources
Semi-Dilute Dumbbells: Solutions of the Fokker–Planck Equation
J, 2021 Spring bead models are commonly used in the constitutive equations for polymer melts. One such model based on kinetic theory—the finitely extensible nonlinear elastic dumbbell model incorporating a Peterlin closure approximation (FENE-P)—has previously ...
Stephen Chaffin, Julia Rees
doaj +1 more source
Fundamental solution of fractional Kolmogorov–Fokker–Planck equation
Examples and Counterexamples, 2021 In this paper, we construct an explicit fundamental solution for the fractional Kolmogorov–Fokker–Planck equation. To achieve this goal, the Fourier transform is applied, and the method of characteristics and the properties of positive definite matrix ...
Cong He +3 more
doaj +1 more source