scholarly journals Fractional Diffusion and Medium Heterogeneity: The Case of the Continuous Time Random Walk

2021 ◽  
pp. 275-286
Author(s):  
Vittoria Sposini ◽  
Silvia Vitali ◽  
Paolo Paradisi ◽  
Gianni Pagnini
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Fractional Diffusion ◽  
Continuous Time Random Walk ◽  
Medium Heterogeneity

CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS

2005 ◽  
Vol 05 (02) ◽  
pp. L291-L297 ◽  
Author(s):  
FRANCESCO MAINARDI ◽  
ALESSANDRO VIVOLI ◽  
RUDOLF GORENFLO
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Continuous Time Random Walk ◽  
Diffusion Limit ◽  
Numerical Comparison ◽  
Time Fractional Diffusion Equation ◽  
Quality Of Approximation

We consider the basic models for anomalous transport provided by the integral equation for continuous time random walk (CTRW) and by the time fractional diffusion equation to which the previous equation is known to reduce in the diffusion limit. We compare the corresponding fundamental solutions of these equations, in order to investigate numerically the increasing quality of approximation with advancing time.

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