Dimension of Riemann-Liouville fractional integral of Takagi function

被引：0
|
作者：
Liu, Ning [1 ]
Yao, Kui [1 ]
Liang, Yong Shun [2 ]
机构：
[1] Army Engn Univ, Inst Sci, Nanjing 211101, Peoples R China
[2] Nanjing Univ Sci & Technol, Inst Sci, Nanjing 210094, Peoples R China
来源：
PROCEEDINGS OF THE 30TH CHINESE CONTROL AND DECISION CONFERENCE (2018 CCDC) | 2018年
基金：
中国国家自然科学基金;
关键词：
fractal function; Box dimension; Hausdorff dimension; Riemann-Liouville fractional integral;
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, we mainly discuss the characteristics of a type of special function called Takagi function which was derived from Weierstrass function. We have proved this function is continuous but can not be differentiable on any subinterval, In other words, it has no hounded variation points even one, Then, we calculate its flausdorff dimension and Box dimension is 1. Furthermore, its Riemann-Liouville fractional integral is also 1. Finally, some numerical and graphic results are provided to characterize Takagi function.
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页码：2376 / 2380
页数：5
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