scholarly journals New Approaches for Solving Fokker Planck Equation on Cantor Sets within Local Fractional Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hassan Kamil Jassim
Keyword(s):  
Fractional Calculus ◽  
Planck Equation ◽  
Cantor Sets ◽  
Fractional Operators ◽  
New Approaches ◽  
Fokker Planck Equation ◽  
Local Fractional Calculus ◽  
Iteration Methods ◽  
Fractional Differential ◽  
Fokker Planck

We discuss new approaches to handling Fokker Planck equation on Cantor sets within local fractional operators by using the local fractional Laplace decomposition and Laplace variational iteration methods based on the local fractional calculus. The new approaches maintain the efficiency and accuracy of the analytical methods for solving local fractional differential equations. Illustrative examples are given to show the accuracy and reliable results.

Brownian Motion on Cantor Sets

2020 ◽  
Vol 21 (3-4) ◽  
pp. 275-281
Author(s):  
Ali Khalili Golmankhaneh ◽  
Saleh Ashrafi ◽  
Dumitru Baleanu ◽  
Arran Fernandez
Keyword(s):  
Brownian Motion ◽  
Classical Method ◽  
Mean Square Displacement ◽  
Planck Equation ◽  
Cantor Sets ◽  
Mean Square ◽  
Fokker Planck Equation ◽  
Fractal Time ◽  
The Mean ◽  
Fokker Planck

AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

scholarly journals Local fractional variational iteration method for Fokker-Planck equation on a Cantor set

2013 ◽  
Vol 23 ◽  
pp. 3-8 ◽  
Author(s):  
Xiao Jun Yang ◽  
Dumitru Baleanu
Keyword(s):  
Iteration Method ◽  
Planck Equation ◽  
Variational Iteration Method ◽  
Cantor Set ◽  
Cantor Sets ◽  
Transform Method ◽  
Variational Iteration ◽  
Fokker Planck Equation ◽  
Fractal Functions ◽  
Fokker Planck

Recently the local fractional operators have started to be considered a useful tool to deal with fractal functions defined on Cantor sets. In this paper, we consider the Fokker-Planck equation on a Cantor set derived from the fractional complex transform method. Additionally, the solution obtained is considered by using the local fractional variational iteration method.

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