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Anomalous Diffusion Models And Mandelbrot Scaling-Law Solutions

Author

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  • XIAO-JUN YANG

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia‡Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea)

  • ABDULRAHMAN ALI ALSOLAMI

    (��Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia)

  • XIAO-JIN YU

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

Abstract

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.

Suggested Citation

  • Xiao-Jun Yang & Abdulrahman Ali Alsolami & Xiao-Jin Yu, 2024. "Anomalous Diffusion Models And Mandelbrot Scaling-Law Solutions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401199
    DOI: 10.1142/S0218348X23401199
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