中文摘要：

给出了Koch曲线的一个复值表达式,并且估计了该表达式的分数阶微积分的分形维数,同时给出了此表达式的Weyl-Marchaud分数阶导数的图像.进一步讨论了Koch曲线的图像与某类自仿分形函数图像的联系.最后证明了这类自仿分形函数的分形维数与其分数阶微积分的分形维数成立着线性关系,一个特殊例子的图像和数值结果在文中给出.

英文摘要：

An analytic expression of von Koch curve has been given.Based on this complex-valued function,we give estimation of fractal dimension of its fractional calculus. Graphs of Weyl-Marchaud fractional derivative of this function have been given. Such function can also be transferred into certain self-affine fractal function.Finally, we set up the linear connection between fractal dimension of this function and order of fractional calculus.Graphs and numerical results of certain examples have been shown.