scholarly journals The fractional diffusion limit of a kinetic model with biochemical pathway

2018 ◽  
Vol 69 (3) ◽  
Author(s):  
Benoît Perthame ◽  
Weiran Sun ◽  
Min Tang
Keyword(s):  
Kinetic Model ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Biochemical Pathway

scholarly journals Generalized fractional Poisson process and related stochastic dynamics

2020 ◽  
Vol 23 (3) ◽  
pp. 656-693 ◽  
Author(s):  
Thomas M. Michelitsch ◽  
Alejandro P. Riascos
Keyword(s):  
Poisson Process ◽  
Continuous Time ◽  
Counting Process ◽  
Stochastic Dynamics ◽  
Waiting Times ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Fractional Operators ◽  
Fractional Poisson Process ◽  
Erlang Process

AbstractWe survey the ‘generalized fractional Poisson process’ (GFPP). The GFPP is a renewal process generalizing Laskin’s fractional Poisson counting process and was first introduced by Cahoy and Polito. The GFPP contains two index parameters with admissible ranges 0 < β ≤ 1, α > 0 and a parameter characterizing the time scale. The GFPP involves Prabhakar generalized Mittag-Leffler functions and contains for special choices of the parameters the Laskin fractional Poisson process, the Erlang process and the standard Poisson process. We demonstrate this by means of explicit formulas. We develop the Montroll-Weiss continuous-time random walk (CTRW) for the GFPP on undirected networks which has Prabhakar distributed waiting times between the jumps of the walker. For this walk, we derive a generalized fractional Kolmogorov-Feller equation which involves Prabhakar generalized fractional operators governing the stochastic motions on the network. We analyze in d dimensions the ‘well-scaled’ diffusion limit and obtain a fractional diffusion equation which is of the same type as for a walk with Mittag-Leffler distributed waiting times. The GFPP has the potential to capture various aspects in the dynamics of certain complex systems.

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.

scholarly journals Fractional Diffusion Limit for Collisional Kinetic Equations

2010 ◽  
Vol 199 (2) ◽  
pp. 493-525 ◽  
Author(s):  
Antoine Mellet ◽  
Stéphane Mischler ◽  
Clément Mouhot
Keyword(s):  
Kinetic Equations ◽  
Fractional Diffusion ◽  
Diffusion Limit

scholarly journals Fractional-Diffusion--Advection Limit of a Kinetic Model

2016 ◽  
Vol 48 (4) ◽  
pp. 2806-2818 ◽  
Author(s):  
Pedro Aceves-Sánchez ◽  
Christian Schmeiser
Keyword(s):  
Kinetic Model ◽  
Fractional Diffusion

scholarly journals Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach

2011 ◽  
Vol 4 (4) ◽  
pp. 873-900 ◽  
Author(s):  
Naoufel Ben Abdallah ◽  
◽  
Antoine Mellet ◽  
Marjolaine Puel ◽  
◽  
...  
Keyword(s):  
Kinetic Equations ◽  
Fractional Diffusion ◽  
Diffusion Limit ◽  
Hilbert Expansion

scholarly journals Heterogeneous discrete kinetic model and its diffusion limit

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ho-Youn Kim ◽  
Yong-Jung Kim ◽  
Hyun-Jin Lim
Keyword(s):  
Kinetic Model ◽  
Diffusion Limit
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