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The Scaling-Law Flows: An Attempt At Scaling-Law Vector Calculus

Author

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  • XIAO-JUN YANG

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China2School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China3Department of Mathematics, Faculty of Science, King AbdulAziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia4Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea)

Abstract

In this paper, the scaling-law vector calculus, which is connected between the vector calculus and the scaling law in fractal geometry, is addressed based on the Leibniz derivative and Stieltjes integral for the first time. The scaling-law Gauss–Ostrogradsky-like, Stokes-like and Green-like theorems, and Green-like identities are considered in sense of the scaling-law vector calculus. The strong and weak conjectures for the scaling-law flows are obtained in detail. The obtained result is a potentially mathematical tool proposed to develop an important way of approaching this challenge for the scaling-law flows.

Suggested Citation

  • Xiao-Jun Yang, 2024. "The Scaling-Law Flows: An Attempt At Scaling-Law Vector Calculus," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401266
    DOI: 10.1142/S0218348X23401266
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