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.
出处
《数学年刊（A辑）》
CSCD
北大核心
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
