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.

中文翻译：

---

标度律流：标度律向量微积分的尝试

本文首次基于莱布尼茨导数和Stieltjes积分解决了连接分形几何中向量微积分和标度律的标度律向量微积分问题。标度律类高斯-奥斯特罗格拉茨基定理、类斯托克斯定理和类格林定理以及类格林恒等式在标度律向量微积分的意义上被考虑。详细获得了标度律流的强猜想和弱猜想。所获得的结果是一种潜在的数学工具，旨在开发一种重要的方法来应对标度律流的这一挑战。