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

Connection Between the Order of Katugampola Fractional Integral and Fractal Dimensions of Weierstrass Function

作　　者：张霞[1] 彭文亮 ZHANG Xia;PENG Wen-liang(Nanjing University of Science and Technology,Nanjing 210094,China;Army University of Engineering of PLA,Nanjing 211101,China)

机构地区：[1]南京理工大学理学院,南京210094 [2]中国人民解放军陆军工程大学基础部,南京211101

出　　处：《大学数学》2019年第2期25-31,共7页College Mathematics

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.

关 键 词：Katugampola分数阶积分 分形维数 WEIERSTRASS函数 

分 类 号：O178[理学—数学]