【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.更多还原

【Abstract】 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.更多还原