Anomalous diffusion modeling by fractal and fractional derivatives

被引：346

作者：

Chen, Wen ^{[1
]}

Sun, Hongguang ^{[1
]}

Zhang, Xiaodi ^{[1
]}

Korosak, Dean ^{[2
]}

机构：

[1] Hohai Univ, Coll Civil Engn, Dept Engn Mech, Inst Soft Matter Mech, Nanjing 210098, Jiangsu, Peoples R China

[2] Univ Maribor, SI-2000 Maribor, Slovenia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Heavy tail; Anomalous diffusion; Fractal derivative; Fractional derivative; Power law; FINITE-DIFFERENCE APPROXIMATIONS; RANDOM-WALK; LAW;

D O I：

10.1016/j.camwa.2009.08.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper makes an attempt to develop a fractal derivative model of anomalous diffusion. We also derive the fundamental solution of the fractal derivative equation for anomalous diffusion, which characterizes a clear power law. This new model is compared with the corresponding fractional derivative model in terms of computational efficiency, diffusion velocity, and heavy tail property. The merits and distinctions of these two models of anomalous diffusion are then summarized. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1754 / 1758

页数：5

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