Let $\Omega$ be a bounded smooth domain of $\mathbb{R}^n$, $0<s<1$ and $(-\Delta)^s$ denotes the restricted fractional Laplacian. Let consider the following fractional Heat equation:

$$ \begin{cases} u_t = (-\Delta)^s u + f(x,t) & \quad \mathrm{in} \Omega \times (0,T),\\ u(x,0)=u_0 & \quad \mathrm{in} \mathbb{R}^N, \\ u(x,t)=0 & \quad \mathrm{in} (\mathbb{R}^N \setminus \Omega )\times (0,T). \end{cases} $$ I want to know that, does $(-\Delta)^s$ generate a semigroup and is it analytic? Is the regularity results for this problem, depending on the regularities of $f(x,t)$ and $u_0$, well-known?

Can someone give a survey of reference for these questions?