Anomalous diffusion: Fractional Fokker–Planck equation and its solutions

2003 ◽  
Vol 44 (5) ◽  
pp. 2179-2185 ◽  
Author(s):  
E. K. Lenzi ◽  
R. S. Mendes ◽  
Kwok Sau Fa ◽  
L. C. Malacarne ◽  
L. R. da Silva
Keyword(s):  
Anomalous Diffusion ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Lévy anomalous diffusion and fractional Fokker–Planck equation

2000 ◽  
Vol 282 (1-2) ◽  
pp. 13-34 ◽  
Author(s):  
V.V. Yanovsky ◽  
A.V. Chechkin ◽  
D. Schertzer ◽  
A.V. Tur
Keyword(s):  
Anomalous Diffusion ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals GENERALIZED WIENER PROCESS AND KOLMOGOROV'S EQUATION FOR DIFFUSION INDUCED BY NON-GAUSSIAN NOISE SOURCE

2005 ◽  
Vol 05 (02) ◽  
pp. L267-L274 ◽  
Author(s):  
ALEXANDER DUBKOV ◽  
BERNARDO SPAGNOLO
Keyword(s):  
White Noise ◽  
Wiener Process ◽  
Anomalous Diffusion ◽  
Gaussian Noise ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Non Gaussian ◽  
Generalized Wiener Process ◽  
Fokker Planck

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker–Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov–Feller equation for discontinuous Markovian processes, and the fractional Fokker–Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.

scholarly journals Green function for a non-Markovian Fokker-Planck equation: comb-model and anomalous diffusion

2009 ◽  
Vol 39 (2a) ◽  
pp. 438-487 ◽  
Author(s):  
L. R. da Silva ◽  
A. A. Tateishi ◽  
M. K. Lenzi ◽  
E. K. Lenzi ◽  
P. C. da Silva
Keyword(s):  
Green Function ◽  
Anomalous Diffusion ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

2011 ◽  
Vol 52 (8) ◽  
pp. 083301 ◽  
Author(s):  
A. T. Silva ◽  
E. K. Lenzi ◽  
L. R. Evangelista ◽  
M. K. Lenzi ◽  
H. V. Ribeiro ◽  
...  
Keyword(s):  
Anomalous Diffusion ◽  
Time Distribution ◽  
First Passage Time ◽  
Planck Equation ◽  
Passage Time ◽  
First Passage ◽  
Fokker Planck Equation ◽  
Fokker Planck
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