豪斯道夫微积分和分数阶微积分模型的分形分析

被引:25
作者
陈文
机构
[1] 河海大学水文水资源与水利工程科学国家重点实验室力学与材料学院软物质力学研究所
基金
国家杰出青年科学基金;
关键词
豪斯道夫导数; 豪斯道夫微积分; 分数阶微积分; 非欧几里得距离; 结构距离; 豪斯道夫分形距离; 基本解;
D O I
10.13340/j.cae.2017.03.001
中图分类号
O172 [微积分];
学科分类号
0701 ; 070101 ;
摘要
清晰解读豪斯道夫微积分和分数阶微积分阶数的分形维意义,并比较这2种微积分建模方法的区别与联系.这是首次清晰定量地导出分数阶微积分的分形几何基础.提供豪斯道夫导数模型描述历史依赖过程的几何解释,即初始时刻依赖性问题,并与分数阶导数模型对比.基于本文作者的早期工作,详细描述非欧几里得距离的豪斯道夫分形距离定义——豪斯道夫导数扩散方程的基本解就是基于该豪斯道夫分形距离.该基本解实质上就是目前广泛使用的伸展高斯分布和伸展指数衰减统计模型.
引用
收藏
页码:1 / 5
页数:5
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