FRACTIONAL ADVECTION-DIFFUSION EQUATION WITH MEMORY AND ROBIN-TYPE BOUNDARY CONDITION

被引：6
|
作者：
Mirza, Itrat Abbas [1 ]
Vieru, Dumitru [2 ]
Ahmed, Najma [3 ]
机构：
[1] Khwaja Fareed Univ Engn & Informat Technol, Rahim Yar Khan, Pakistan
[2] Tech Univ Gheorghe Asachi Iasi, Iasi, Romania
[3] Govt Coll Univ, Abdus Salam Sch Math Sci, Lahore, Pakistan
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2019年 / 14卷 / 03期
关键词：
Advection; diffusion; Caputo derivative; analytical solution; APPROXIMATE SOLUTION; ALGORITHM;
D O I：
10.1051/mmnp/2018075
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The one-dimensional fractional advection-diffusion equation with Robin-type boundary conditions is studied by using the Laplace and finite sine-cosine Fourier transforms. The mathematical model with memory is developed by employing the generalized Fick's law with time-fractional Caputo derivative. The influence of the fractional parameter (the non-local effects) on the solute concentration is studied. It is found that solute concentration can be minimized by decreasing the memory parameter. Also, it is found that, at small values of time the ordinary model leads to minimum concentration, while at large values of the time the fractional model is recommended.
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页数：13
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