On the connection between the order of the fractional derivative and the Hausdorff dimension of a fractal function

被引：21

作者：

Yao, K. ^{[2
,3
,4
]}

Liang, Y. S. ^{[1
]}

Zhang, F. ^{[5
]}

机构：

[1] Nanjing Univ Sci & Technol, Sch Sci, Nanjing 210094, Peoples R China

[2] Nanjing Normal Univ, Dept Math, Nanjing 210097, Peoples R China

[3] Chuzhou Univ, Inst Math, Chuzhou 239000, Peoples R China

[4] PLAUST, Inst Sci, Nanjing 210000, Peoples R China

[5] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2009年 / 41卷 / 05期

关键词：

E-INFINITY THEORY; NONLINEAR DYNAMICS; PREREQUISITES; CALCULUS;

D O I：

10.1016/j.chaos.2008.09.053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates the fractional derivative of a fractal function. It has been proven that there exists certain linear connection between the order of the Weyl-Marchaud fractional derivatives(WMFD) and the Hausdorff dimension of a fractal function. Graphs and numerical results further show this linear relationship. Crown Copyright (C) 2008 Published by Elsevier Ltd. All rights reserved.

引用

页码：2538 / 2545

页数：8

共 16 条

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