In this paper, we mainly research on Hadamard fractional integral of Besicovitch function. A series of propositions of Hadamard fractional integral of [Formula: see text] have been proved first. Then, we give some fractal dimensions of Hadamard fractional integral of Besicovitch function including Box dimension, [Formula: see text]-dimension and Packing dimension. Finally, relationship between the order of Hadamard fractional integral and fractal dimensions of Besicovitch function has also been given.

中文翻译：

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贝斯科维奇函数分形维数与哈达玛分形积分阶的关系

本文主要研究Besicovitch函数的Hadamard分数积分。[公式：见正文]的Hadamard分数积分的一系列命题首先得到了证明。然后，我们给出了Besicovitch函数的Hadamard分数积分的一些分形维数，包括Box维数、[公式：见正文]-维数和Packing维数。最后，还给出了Hadamard分数阶积分与Besicovitch函数分形维数的关系。