The anomalous diffusion model based on a fractional calculus approach applied to describe the rehydration process of dried vegetal food matrices

2021 ◽  
Author(s):  
Roberto Lemus‐Mondaca ◽  
Helena Nuñez ◽  
Aldonza Jaques ◽  
Cristian Ramírez ◽  
Ricardo Simpson
Keyword(s):  
Fractional Calculus ◽  
Diffusion Model ◽  
Anomalous Diffusion ◽  
Model Based ◽  
Food Matrices ◽  
Rehydration Process

scholarly journals Discrete fractional diffusion model with two memory terms

2015 ◽  
Vol 19 (4) ◽  
pp. 1177-1181
Author(s):  
Yan-Mei Qin ◽  
Hua Kong ◽  
Kai-Teng Wu ◽  
Xiao-Ming Zhu
Keyword(s):  
Numerical Simulation ◽  
Fractional Calculus ◽  
Diffusion Model ◽  
Discrete Time ◽  
Anomalous Diffusion ◽  
Fractional Diffusion ◽  
Fractional Difference ◽  
Linear Evolution ◽  
Time Domains ◽  
Diffusion Behaviors

Fractional calculus can always exactly describe anomalous diffusion. Recently the discrete fractional difference is becoming popular due to the depiction of non-linear evolution on discrete time domains. This paper proposes a diffusion model with two terms of discrete fractional order. The numerical simulation is given to reveal various diffusion behaviors.

scholarly journals Research on Rock Creep Characteristics Based on the Fractional Calculus Meshless Method

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Gang Peng ◽  
Zhanqing Chen ◽  
Jiarui Chen
Keyword(s):  
Fractional Calculus ◽  
Meshless Method ◽  
Test System ◽  
Constitutive Relationship ◽  
Creep Process ◽  
Kelvin Model ◽  
Related Data ◽  
Model Based ◽  
Rock Creep ◽  
Generalized Kelvin Model

The application of fractional calculus in the rheological problems has been widely accepted. In this study, the constitutive relationship of the generalized Kelvin model based on fractional calculus was studied, and the meshless method was introduced so as to derive a new meshless algorithm formula based on the fractional calculus of the generalized Kelvin model. By using the MTS815.02 hydraulic servo rock mechanics test system, the creep test of mudstones is carried out, and the related data of the creep process were obtained. Based on the generalized Kelvin model of fractional calculus, the related creep parameters of the argillaceous sandstone under compression were fitted. The results showed that the solution of the generalized Kelvin model based on fractional calculus was greatly consistent with the numerical method solution. Meanwhile, the meshless algorithm based on fractional calculus had a favorable stability and accuracy.

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