一类分形函数的Weyl-Marchaud分数阶导数的Hausdorff维数  

The Hausdorff Dimension of Weyl-Marchaud Fractional Derivative of a Type of Fractal Functions

作　　者：母雷 姚奎[1] 邱华[2] 苏维宜[2] 

机构地区：[1]解放军理工大学理学院,南京211101 [2]南京大学数学系,南京210093

出　　处：《数学年刊（A辑）》2017年第3期257-264,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11471157)的资助

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.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.

关 键 词：HAUSDORFF维数 广义Weierstrass型函数 Weyl-Marchaud分数阶导数 线性关系 

分 类 号：O189[理学—数学]