关于一类函数及其分数阶微积分函数的分形维数

On the Fractal Dimensions of a Function and Its Fractional Calculus Functions

将经典的Weierstrass型函数中的函数项扩展为一般的李卜希兹连续周期函数,在指数参数大于等于1的情况下讨论了这类函数及其分数阶微积分函数,得出原函数及其分数阶积分函数图像的分形维数均为1,并给出其分数阶微分函数图像维数的上下界估计。同时,利用Matlab绘制出不同α值的函数图像,使结果更直观。

The function term in classical Weierstrass-type functions was extended to the general Lipschitz continuous periodic function, and such a function and its fractional calculus functions in case of the index parameter greater than or equal to 1 were discussed. The fractal dimensions of the graphs of the original function and its fractional differential function were obtained. Mean while, by using the Matlab, their graphs with different α values were drawn to make the results more intuitive.