  The global well-posedness of the smooth solution to the three-dimensional
(3D) incompressible micropolar equations is a difficult open problem. This
paper focuses on the 3D incompressible micropolar equations with fractional
dissipations $( \Delta)^{\alpha}u$ and $(-\Delta)^{\beta}w$.Our objective is to
establish the global regularity of the fractional micropolar equations with the
minimal amount of dissipations. We prove that, if $\alpha\geq \frac{5}{4}$,
$\beta\geq 0$ and $\alpha+\beta\geq\frac{7}{4}$, the fractional 3D micropolar
equations always possess a unique global classical solution for any
sufficiently smooth data. In addition, we also obtain the global regularity of
the 3D micropolar equations with the dissipations given by Fourier multipliers
that are logarithmically weaker than the fractional Laplacian.
