Abstract This paper introduces the notion of “fractional fractals”. The main idea is to establish a connection between the classical iterated function system and the first order truncation of the Gründwald-Letnikov fractional derivative. This allows us to consider higher order truncations, and also to study the limit sets for these higher order systems. We prove several results involving the existence and dimension of such limit sets, that will be called “fractional fractals”. Some numerical calculations and representations illustrate relevant examples.

中文翻译：

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分数形

摘要 本文介绍了“分形”的概念。主要思想是在经典迭代函数系统和 Gründwald-Letnikov 分数阶导数的一阶截断之间建立联系。这使我们能够考虑高阶截断，并研究这些高阶系统的极限集。我们证明了涉及这种极限集的存在性和维数的几个结果，这将被称为“分形”。一些数值计算和表示说明了相关的例子。