scholarly journals An Investigation of Methanol Anomalous Diffusion in Mesoporous Silica

2016 ◽  
Vol 17 (3) ◽  
pp. 426-429
Author(s):  
A.A. Zhokh ◽  
P.E. Strizhak
Keyword(s):  
Experimental Data ◽  
Mesoporous Silica ◽  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Kinetic Data ◽  
Fractional Diffusion ◽  
Diffusive Regime ◽  
Methanol Transport ◽  
Time Fractional Diffusion Equation ◽  
Good Manner

Methanol transport in mesoporous silica is investigated. It is demonstrated that usual approach based on the second Fick’s law fails describing the experimental kinetic data. Contrary, the solution of the time-fractional diffusion equation fits the experimental data in a fairly good manner. Obtained value of the fractional order reveals the presence of fast super-diffusive regime of transport.

scholarly journals Unique continuation principle for the one-dimensional time-fractional diffusion equation

2019 ◽  
Vol 22 (3) ◽  
pp. 644-657 ◽  
Author(s):  
Zhiyuan Li ◽  
Masahiro Yamamoto
Keyword(s):  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Function Method ◽  
Unique Continuation ◽  
Fractional Diffusion ◽  
Uniqueness Of Solutions ◽  
One Dimensional ◽  
Continuation Principle ◽  
Time Fractional Diffusion Equation ◽  
The One

Abstract This paper deals with the unique continuation of solutions for a one-dimensional anomalous diffusion equation with Caputo derivative of order α ∈ (0, 1). Firstly, the uniqueness of solutions to a lateral Cauchy problem for the anomalous diffusion equation is given via the Theta function method, from which we further verify the unique continuation principle.

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