In this paper, we introduce the notions of equiaffine arclength and curvature with fractional order for a plane curve and compare them with the standard ones. By using these definitions, we obtain an equiaffine Frenet formula and then construct an analogue of the fundamental theorem. The plane curves of constant equiaffine curvature with fractional order are classified. Several examples are also illustrated.

中文翻译：

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分数阶微积分在等仿射几何中的应用：分数阶平面曲线

在本文中，我们介绍了平面曲线的分数阶等仿射弧长和曲率的概念，并将它们与标准曲线进行了比较。通过使用这些定义，我们获得了等仿射 Frenet 公式，然后构造了基本定理的类似物。对具有分数阶次的等仿射曲率的平面曲线进行了分类。还举例说明了几个例子。