On the local fractional derivative of everywhere non-differentiable continuous functions on intervals
作者： Cheng-shi Liu
DOI: 10.1016/J.CNSNS.2016.05.029
关键词:
摘要: We first prove that for a continuous function f(x) defined on an open interval, the Kolvankar-Gangal’s (or equivalently Chen-Yan-Zhang’s) local fractional derivative f(α)(x) is not continuous, and then it impossible KG exists everywhere interval satisfies ≠ 0 in same time. In addition, we give criterion of nonexistence non-differentiable functions. Furthermore, construct two simple nowhere differentiable functions (0, 1) they have no derivatives everywhere.
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