特慢扩散的一种分数阶结构导数模型

陈文; 黑鑫东; 梁英杰

doi:10.3879/j.issn.1000-0887.2016.06.005

特慢扩散的一种分数阶结构导数模型

doi: 10.3879/j.issn.1000-0887.2016.06.005

陈文^1,2,
黑鑫东^1,2,
梁英杰^1,2

¹水文水资源与水利工程科学国家重点实验室(河海大学),南京 210098;²河海大学力学与材料学院,南京 211100

基金项目: 国家自然科学基金（面上项目)(11372097)；111引智计划（B12032）

详细信息

作者简介:
陈文（1967—），男，教授，博士，博士生导师(通讯作者. E-mail: chenwen@hhu.edu.cn)；黑鑫东（1988—），男，博士生（E-mail: heixindong@hhu.edu.cn）；梁英杰（1988—），男，博士生（E-mail: liangyj1989@126.com）.

中图分类号: O39;O352;O371;O175.2
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- 被引次数: 0
出版历程
- 收稿日期: 2016-01-25
- 修回日期: 2016-03-04
- 刊出日期: 2016-06-15

A Fractional Structural Derivative Model for Ultra-Slow Diffusion

¹State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering(Hohai University), Nanjing 210098, P.R.China;²College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11372097)

摘要

摘要: 自然界和工程中存在很多比幂率慢扩散（sub-diffusion）过程更慢的扩散，即特慢扩散（ultra-slow diffusion）.特慢扩散难以用传统的反常扩散建模方法来描述.Sinai(西奈)随机模型描述了一种特殊的对数关系特慢扩散.运用Mittag-Leffler（米塔格-累夫勒）函数的反函数，将Sinai扩散拓展为一般的特慢扩散.此外，该文的模型引入初始状态参量，解决了Sinai对数扩散不适用于初始时刻附近的问题.作为分数阶导数的一般情况，该文也引入了分数阶结构导数的概念，并用来建立特慢扩散的控制微分方程.
- 特慢扩散 /
- Sinai随机模型 /
- Mittag-Leffler反函数 /
- 分数阶结构导数 /
- 扩散方程
Abstract: The ultra-slow diffusion is even more slow than the power-law sub-diffusion and is widely observed in a variety of natural and engineering fields. The ultra-slow diffusion cannot be well described with the traditional anomalous diffusion models. The Sinai’s law of diffusion depicts a special type of ultra-slow diffusion which is characterized by a logarithmic stochastic relationship. In this study, the Sinai diffusion was extended to a general ultra-slow diffusion. In addition, in the proposed model the initial parameters were introduced to remedy the perplexing issue that the Sinai diffusion was not feasible around the initial period of the ultra-slow diffusion. As a generalized fractional-order derivative, the concept of the fractional structural derivative was also presented to establish the partial differential equation governing the ultra-slow diffusion.
- ultra-slow diffusion /
- Sinai stochastic model /
- inverse Mittag-Leffler function /
- fractional structural derivative /
- diffusion equation

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参考文献(14)

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