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

scholarly journals Determination of the order of fractional derivative for subdiffusion equations

2020 ◽  
Vol 23 (6) ◽  
pp. 1647-1662
Author(s):  
Ravshan Ashurov ◽  
Sabir Umarov
Keyword(s):  
Fractional Derivative ◽  
Fixed Time ◽  
Time Instant ◽  
Observation Data ◽  
Additional Information ◽  
Fractional Modeling ◽  
Time Fractional Derivative ◽  
The Right ◽  
Right Order

Abstract The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.

scholarly journals Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model

2018 ◽  
Vol 29 (3) ◽  
pp. 035701 ◽  
Author(s):  
Hongmei Zhang ◽  
Qing zhe Zhang ◽  
Litao Ruan ◽  
Junbo Duan ◽  
Mingxi Wan ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Fractional Derivative Model

Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials

AIAA Journal ◽  
1995 ◽  
Vol 33 (3) ◽  
pp. 547-550 ◽  
Author(s):  
Lloyd B. Eldred ◽  
William P. Baker ◽  
Anthony N. Palazotto
Keyword(s):  
Fractional Derivative ◽  
Constitutive Relations ◽  
Viscoelastic Materials ◽  
Fractional Derivative Model
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