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中文摘要：
自然界存在诸多的非光滑现象，如海岸线、岩石的裂隙和截面形貌等．经典的微积分理论和欧氏几何中的常用方法无法用来刻画其可微性．局部分数阶导数是局部化的分数阶导算子，是潜在的研究非光滑曲线微尺度性态的工具之一．本文首先回顾了基于分数阶积分和类Cantor集生成的阶梯曲线，然后利用一般的二项式展开，从分数阶可微函数的角度得到了非光滑热曲线的分数阶次可微性．
英文摘要：
There are many non-smooth objects in nature, such as coastline, rock fracture, cross section, whose differentiabilities cannot be described by ordinary calculus and methods in Euclidean geometry. The local fractional derivative is one of the potential tools to investigate the non-smooth problems. This study revisits the non-smooth curves generated from the fractional integrals and Cantor-like set. From the view of the fractional differentiable functions, the differentiabilities of the non-smooth curves are derived by using a binomial expansion.
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