自仿函数分数阶导数的分形维数

姚奎, 梁永顺, 苏维宜, 姚泽清

数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 693-698.

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数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 693-698. DOI: 10.12386/A2013sxxb0069
论文

自仿函数分数阶导数的分形维数

    姚奎1, 梁永顺2, 苏维宜3, 姚泽清1
作者信息 +

Dimension of Graphs of Fractional Derivatives of Self-Affine Curves

    Kui YAO1, Yong Shun LIANG2, Wei Yi SU3, Ze Qing YAO1
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摘要

研究一类自仿函数的分数阶导数,获得了自仿函数的Weyl-Marchaud分数阶导数的图像盒维数,证明了分数阶导数的阶与分形维数之间的线性关系.

Abstract

This paper investigates the fractional derivatives of self-affine fractal curves. The upper box-counting dimension of the graphs of self-affine curves is obtained. It shows that differentiation of fractional order increases the dimension of self-affine curves.

关键词

自仿射曲线 / 分数阶导数 / 分形维数

Key words

self-affine curves / fractional derivatives / fractal dimension

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姚奎, 梁永顺, 苏维宜, 姚泽清. 自仿函数分数阶导数的分形维数. 数学学报, 2013, 56(5): 693-698 https://doi.org/10.12386/A2013sxxb0069
Kui YAO, Yong Shun LIANG, Wei Yi SU, Ze Qing YAO. Dimension of Graphs of Fractional Derivatives of Self-Affine Curves. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 693-698 https://doi.org/10.12386/A2013sxxb0069

参考文献

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基金

国家自然科学基金资助项目(11071282, 11201230, 10571084),湘潭大学教育部智能计算与信息处理重点实验室开放课题项目(2011ICIP07)

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