  In the article 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 Smales 15th Problem (one of
the Millennium Prize Problems for the Navier--Stokes equations) is also
addressed.
