This paper concentrates on discussing the properties of Riemann–Liouvile fractional (RLF) calculus of two special continuous functions. The first type proves the non-differentiability of a special continuous function that does not satisfy Hölder condition, and the second type uses fractal iteration to construct a fractal function defined on [0, 1] with unbounded variation. Then we calculate RLF integral and RLF derivative of this special function, and give the corresponding numerical calculation results and the corresponding function image.

中文翻译：

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关于某些连续函数的分数可微性的进一步讨论

本文集中讨论了两个特殊连续函数的黎曼-刘维尔分数 (RLF) 微积分的性质。第一种证明了不满足Hölder条件的特殊连续函数的不可微性，第二种使用分形迭代构造了定义在[0, 1]具有无限的变化。然后我们计算这个特殊函数的RLF积分和RLF导数，并给出相应的数值计算结果和相应的函数图像。