一类Weierstrass型函数的分数阶W-M导数图象的分形维数  

The Fractal Dimension of Graph of the W-M Fractional Derivative of the Weierstrass-type Function

作　　者：李红娟[1] 

机构地区：[1]太原理工大学理学院,太原030024

出　　处：《太原理工大学学报》2011年第6期665-668,共4页Journal of Taiyuan University of Technology

基　　金：太原理工大学校青年基金资助项目(K201036)

摘　　要：通过对Weierstrass型函数变形,考虑了一类广义的Weierstrass型函数,这类分形函数图象的维数已求出,在此基础上应用Weyl-Marchaud分数阶导数(简称"W-M导数")的定义进一步求出了这类分形函数的分数阶导函数图像的维数。In the paper,by means of deforming Weierstrass function,we considered a kind of generalized Weierstrass-type function,of which the fractal dimension of graph has been calculated.On that basis,We applied the definition of the Weyl-Marchaud fractional derivative to calculate the fractal dimension of graph of the Weyl-Marchaud fractional derivative of the Weierstrass-type function.

关 键 词：Weierstrass型函数 ν阶分数阶Weyl-Marchaud导数 K-维数 

分 类 号：O189.12[理学—数学]