Katugampola分数阶积分的阶与Weierstrass函数的分形维数之间的关系（英文）

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英文篇名：Connection Between the Order of Katugampola Fractional Integral and Fractal Dimensions of Weierstrass Function 作者：张霞 ; 彭文亮 英文作者：ZHANG Xia;PENG Wen-liang;Nanjing University of Science and Technology;Army University of Engineering of PLA; 关键词：Katugampola分数阶积分 ; 分形维数 ; Weierstrass函数 英文关键词：Katugampola fractional integral;;Fractal dimensions;;Weierstrass function 中文刊名：GKSX 英文刊名：College Mathematics 机构：南京理工大学理学院;中国人民解放军陆军工程大学基础部; 出版日期：2019-04-15 出版单位：大学数学 年：2019 期：v.35;No.202 语种：英文; 页：GKSX201902007 页数：7 CN：02 ISSN：34-1221/O1 分类号：29-35

摘要

计算Weierstrass函数的Katugampola分数阶积分的分形维数,如盒维数、K-维数和P-维数.证明了Weierstrass函数的Katugampola分数阶积分的阶与Weierstrass函数的分形维数之间存在线性关系.
        We investigate fractal dimensions of Katugampola fractional integral of Weierstrass function defined on a closed interval. Fractal dimensions such as Box dimension, K-dimension and Packing dimension are calculated. Furthermore, we get the result that there exists some linear relationship between the order of Katugampola fractional integral and fractal dimensions of Weierstrass function.

引文

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