Abstract
In the paper, we suggest the Hausdorff vector calculus based on the Chen Hausdorff calculus for the first time. The Gauss–Ostrogradsky-like, Stokes-like, and Green-like theorems, and Green-like identities are obtained in the framework of the Hausdorff vector calculus. The formula is proposed as a mathematical tool to describe the real-world problems for the fractal power-law flow equations with the anomalous diffusion equation. A conjecture for the fractal power-law flow equations analogous to the Smale’s 15th problem and one of Millennium Prize Problems for the Navier–Stokes equations is also addressed.