| 母雷,姚奎,邱华,苏维宜.一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数[J].数学年刊A辑,2017,38(3):257~264 |
| 一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数 |
| The Hausdorff Dimension of Weyl-Marchaud Fractional Derivative of a Type of Fractal Functions |
| Received:September 14, 2015 Revised:March 05, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0020 |
| 中文关键词: Hausdorff dimension, Generalized Weierstrass-type functions, |
| 英文关键词:Hausdorff dimension, Generalized Weierstrass-type functions, |
| 基金项目:本文受到国家自然科学基金(No.11471157)的资助. |
| Author Name | Affiliation | E-mail | | MU Lei | Institute of Science, PLA University of Science and Technology, Nanjing 211101, China. | mulei_fractal@sina.com | | YAO Kui | Corresponding author. Institute of Science, PLA University of Science and Technology, Nanjing 211101, China. | flyyaok@sina.com | | QIU Hua | Department of Mathematics, Nanjing University, Nanjing 210093, China. | huaqiu@nju.edu.cn | | SU Weiyi | Department of Mathematics, Nanjing University, Nanjing 210093, China. | suqiu@nju.edu.cn |
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| 中文摘要: |
| 首先介绍广义Weierstrass型函数的Weyl-Marchaud分数阶导数, 得到了带随机相位的广义Weierstrass型函数的Weyl-Marchaud分数阶导数图像的Hausdorff维数, 证明了该分形函数图像的Hausdorff维数与Weyl-Marchaud分数阶导数的阶之间的线性关系. |
| 英文摘要: |
| This paper firstly introduces the Weyl-Marchaud fractional
derivative of the generalized Weierstrass-type functions, then gets the
Hausdorff dimension of the graphs of the fractional derivative of
Weierstrass-type functions with arbitrary phases, proves the linear
relationship between the order of the Weyl-Marchaud fractional derivative
and Hausdorff dimension of the fractal functions. |
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