In this paper, the anomalous diffusion models are studied in the framework of the scaling-law calculus with the Mandelbrot scaling law. A analytical technology analogous to the Fourier transform is proposed to deal with the one-dimensional scaling-law diffusion equation. The scaling-law series formula via Kohlrausch–Williams–Watts function is efficient and accurate for finding exact solutions for the scaling-law PDEs arising in the Mandelbrot scaling-law phenomena.

中文翻译：

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反常扩散模型和曼德尔布罗特标度律解

本文在曼德尔布罗特标度律的标度律微积分框架下研究了反常扩散模型。提出了一种类似于傅立叶变换的解析技术来处理一维标度律扩散方程。通过 Kohlrausch-Williams-Watts 函数的标度律级数公式对于找到 Mandelbrot 标度律现象中出现的标度律偏微分方程的精确解非常高效且准确。