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

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.