Derivation and numerical validation of the fundamental solutions for constant and variable-order structural derivative advection-dispersion models

被引：6

作者：

Wang, Fajie ^{[1
,2
]}

Cai, Wei ^{[3
]}

Zheng, Bin ^{[4
]}

Wang, Chao ^{[1
]}

机构：

[1] Qingdao Univ, Natl Engn Res Ctr Intelligent Elect Vehicle Power, Sch Electromech Engn, Qingdao 266071, Peoples R China

[2] Qingdao Univ, Inst Mech Multifunct Mat & Struct, Qingdao 266071, Peoples R China

[3] Hohai Univ, Coll Mech & Elect Engn, Changzhou 213022, Jiangsu, Peoples R China

[4] Hohai Univ, Coll Mech & Mat, Nanjing 210098, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2020年 / 71卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Anomalous diffusion; Structural derivative; Fundamental solutions; Kernel functions; ANOMALOUS DIFFUSION; LOCALIZED METHOD;

D O I：

10.1007/s00033-020-01360-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Various non-local structural derivative diffusion models have been proposed based on different kernel functions to describe the anomalous time dependence of the mean-squared displacements. In the present study, the fundamental solutions for constant and variable-order structural derivative advection-dispersion models are achieved via scaling transformation and the generalized non-Euclidean Hausdorff fractal distance. Comparative numerical investigations of the structural derivative models have been conducted to reveal the influences of various kernels via the meshless method of fundamental solutions. Numerical results verify the validity of the derived fundamental solutions and the rationality of the employed numerical method for structural derivative advection-dispersion models.

引用

页数：18

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