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<p>This paper studies the effect of the Liouville fractional integral on the box dimension of the graph of a function. Using wavelet methods, we prove that if a function satisfies both Hölder and anti-Hölder conditions on a bounded interval, then the box dimension of its graph decreases linearly with the order of fractional integration. We also establish several auxiliary criteria for estimating the box dimension of graphs.</p>

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Effects of Liouville fractional integral on functions with Hölder and anti-Hölder conditions I: wavelet decomposition

  • 期刊论文

  • 发表日期：

    2026年4月23日

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  • Peizhi Liu,
  • Yongshun Liang

摘要

This paper studies the effect of the Liouville fractional integral on the box dimension of the graph of a function. Using wavelet methods, we prove that if a function satisfies both Hölder and anti-Hölder conditions on a bounded interval, then the box dimension of its graph decreases linearly with the order of fractional integration. We also establish several auxiliary criteria for estimating the box dimension of graphs.