Abstract In this paper, we consider a Takagi-like function on 2-series field and give its 2-adic derivatives by applying Vladimirov operator. The 2-adic derivatives of Takagi-like function with order 0 < α < 1 exist and show some fractal feature. Furthermore, both box dimension and Hausdorff dimension of the graph of its derivatives are obtained and equal to 1 + α.

中文翻译：

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2-级数域上Takagi-like函数的2-adic导数和分形维数

摘要 在本文中，我们考虑了 2 级数域上的 Takagi-like 函数，并应用 Vladimirov 算子给出了它的 2-adic 导数。存在阶次为 0 < α < 1 的 Takagi-like 函数的 2-adic 导数并表现出一些分形特征。此外，获得了其导数图的框维和豪斯多夫维，并且都等于 1 + α。