scholarly journals A New Approach to Time-Dependent Solutions to the Non-Linear Fokker-Planck Equations Related to Arbitrary Functions of Tsallis Entropy: A Mathematical Study and Investigation

2012 ◽  
Vol 03 (05) ◽  
pp. 420-429
Author(s):  
Alireza Heidari ◽  
Seyedali Vedad ◽  
Mohammadali Ghorbani
Keyword(s):  
Tsallis Entropy ◽  
Time Dependent ◽  
Mathematical Study ◽  
New Approach ◽  
Non Linear ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals Non-Linear Langevin and Fractional Fokker–Planck Equations for Anomalous Diffusion by Lévy Stable Processes

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 760 ◽  
Author(s):  
Johan Anderson ◽  
Sara Moradi ◽  
Tariq Rafiq
Keyword(s):  
Anomalous Diffusion ◽  
Transport Coefficient ◽  
Numerical Solutions ◽  
Distribution Functions ◽  
Space Distribution ◽  
Non Linear ◽  
Non Local ◽  
Local Transport ◽  
Fokker Planck Equations ◽  
Fokker Planck

The numerical solutions to a non-linear Fractional Fokker–Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The aim is to model anomalous diffusion using an FFP description with fractional velocity derivatives and Langevin dynamics where Lévy fluctuations are introduced to model the effect of non-local transport due to fractional diffusion in velocity space. Distribution functions are found using numerical means for varying degrees of fractionality of the stable Lévy distribution as solutions to the FFP equation. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy and modified transport coefficient. The transport coefficient significantly increases with decreasing fractality which is corroborated by analysis of experimental data.

scholarly journals Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy

Entropy ◽  
2011 ◽  
Vol 13 (11) ◽  
pp. 1928-1944 ◽  
Author(s):  
Mauricio S. Ribeiro ◽  
Fernando D. Nobre ◽  
Evaldo M. F. Curado
Keyword(s):  
Tsallis Entropy ◽  
Fokker Planck Equations ◽  
Fokker Planck
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