scholarly journals Fractional Fokker-Planck equation in a fractal medium

2020 ◽  
Vol 24 (4) ◽  
pp. 2589-2595
Author(s):  
Shuxian Deng ◽  
Xinxin Ge
Keyword(s):  
Fourier Transform ◽  
Heat Conduction ◽  
Darboux Transformation ◽  
Planck Equation ◽  
Fractal Medium ◽  
Fokker Planck Equation ◽  
Fokker Planck

This paper studies a fractal modification of Fokker-Planck equation for a heat conduction in a fractal medium. Fourier transform and Darboux transformation are used to solve the equation, some new results are obtained.

scholarly journals Extended Mellin integral representations for the absolute value of the gamma function

Analysis ◽  
2018 ◽  
Vol 38 (1) ◽  
pp. 11-20
Author(s):  
Nicolas Privault
Keyword(s):  
Fourier Transform ◽  
Gamma Function ◽  
Bessel Functions ◽  
Planck Equation ◽  
Integral Representations ◽  
Modified Bessel Functions ◽  
Absolute Value ◽  
Fokker Planck Equation ◽  
The Absolute ◽  
Fokker Planck

AbstractWe derive Mellin integral representations in terms of Macdonald functions for the squared absolute value{s\mapsto|\Gamma(a+is)|^{2}}of the gamma function and its Fourier transform when{a<0}is non-integer, generalizing known results in the case{a>0}. This representation is based on a renormalization argument using modified Bessel functions of the second kind, and it applies to the representation of the solutions of a Fokker–Planck equation.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

Sign in / Sign up

Export Citation Format

Share Document