A distributed-order time fractional derivative model for simulating bimodal sub-diffusion in heterogeneous media

2020 ◽  
Vol 591 ◽  
pp. 125504
Author(s):  
Maosheng Yin ◽  
Rui Ma ◽  
Yong Zhang ◽  
Song Wei ◽  
Geoffrey R. Tick ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Heterogeneous Media ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative ◽  
Distributed Order

Can a Time Fractional-Derivative Model Capture Scale-Dependent Dispersion in Saturated Soils?

Ground Water ◽  
2017 ◽  
Vol 55 (6) ◽  
pp. 857-870 ◽  
Author(s):  
Rhiannon M. Garrard ◽  
Yong Zhang ◽  
Song Wei ◽  
HongGuang Sun ◽  
Jiazhong Qian
Keyword(s):  
Fractional Derivative ◽  
Saturated Soils ◽  
Fractional Derivative Model ◽  
Time Fractional Derivative

Fast Mixing in Heterogeneous Media Characterized by Fractional Derivative Model

2020 ◽  
Vol 134 (2) ◽  
pp. 387-397
Author(s):  
Yingjie Liang ◽  
Zhi Dou ◽  
Lizhou Wu ◽  
Zhifang Zhou
Keyword(s):  
Fractional Derivative ◽  
Heterogeneous Media ◽  
Fractional Derivative Model

scholarly journals Analytical Solutions of the Diffusion–Wave Equation of Groundwater Flow with Distributed-Order of Atangana–Baleanu Fractional Derivative

2021 ◽  
Vol 11 (9) ◽  
pp. 4142
Author(s):  
Nehad Ali Shah ◽  
Abdul Rauf ◽  
Dumitru Vieru ◽  
Kanokwan Sitthithakerngkiet ◽  
Poom Kumam
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Groundwater Flow ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Integral Transforms ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Time Fractional Derivative ◽  
Distributed Order

A generalized mathematical model of the radial groundwater flow to or from a well is studied using the time-fractional derivative with Mittag-Lefler kernel. Two temporal orders of fractional derivatives which characterize small and large pores are considered in the fractional diffusion–wave equation. New analytical solutions to the distributed-order fractional diffusion–wave equation are determined using the Laplace and Dirichlet-Weber integral transforms. The influence of the fractional parameters on the radial groundwater flow is analyzed by numerical calculations and graphical illustrations are obtained with the software Mathcad.

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