  We consider the nonlinear half laplacian heat equation $$
  u_t+(-\Delta)^{\frac{1}{2}} u-|u|^{p-1}u=0,\quad \mathbb{R}^n\times (0, T).
  $$ We prove that all blows-up are type I, provided that $n \leq 4$ and $
1<p<p_{*} (n)$ where $ p_{*} (n)$ is an explicit exponent which is below
$\frac{n+1}{n-1}$, the critical Sobolev exponent. Central to our proof is a
Giga-Kohn type monotonicity formula for half laplacian and a Liouville type
theorem for self-similar nonlinear heat equation. This is the first instance of
a monotonicity formula at the level of the nonlocal equation, without invoking
the extension to the half-space.
