| 一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数 |
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| 引用本文： | 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(中文版),2017,38(3):257-264. |
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| 作者姓名： | 母雷 姚奎 邱华 苏维宜 |
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| 作者单位： | 解放军理工大学理学院, 南京 211101.,通讯作者. 解放军理工大学理学院, 南京 211101.,南京大学数学系, 南京 210093.,南京大学数学系, 南京 210093. |
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| 基金项目： | 本文受到国家自然科学基金(No.11471157)的资助. |
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| 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.
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| 关 键 词： | Hausdorff dimension Generalized Weierstrass-type functions |
| 收稿时间： | 2015/9/14 0:00:00 |
| 修稿时间： | 2016/3/5 0:00:00 |
The Hausdorff Dimension of Weyl-Marchaud Fractional Derivative of a Type of Fractal Functions |
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| MU Lei,YAO Kui,QIU Hua and SU Weiyi.The Hausdorff Dimension of Weyl-Marchaud Fractional Derivative of a Type of Fractal Functions[J].Chinese Annals of Mathematics,2017,38(3):257-264. |
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| Authors: | MU Lei YAO Kui QIU Hua and SU Weiyi |
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| Institution: | Institute of Science, PLA University of Science and Technology, Nanjing 211101, China.,Corresponding author. Institute of Science, PLA University of Science and Technology, Nanjing 211101, China.,Department of Mathematics, Nanjing University, Nanjing 210093, China. and Department of Mathematics, Nanjing University, Nanjing 210093, China. |
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| Abstract: | 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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| Keywords: | Hausdorff dimension Generalized Weierstrass-type functions |
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