  In this paper, we study quantitative spatial analytic bounds and unique
continuation inequalities of solutions for fractional heat equations with an
analytic lower order term on the whole space. At first, we show that the
solution has a uniform positive analytic radius for all time, and the solution
enjoys a log-type ultra-analytic bound if the coefficient is ultra-analytic.
Second, we prove a H\"{o}lder type interpolation inequality on a thick set,
with an explicit dependence on the analytic radius of coefficient. Finally, by
the telescoping series method, we establish an observability inequality from a
thick set. As a byproduct of the proof, we obtain observability inequalities in
weighted spaces from a thick set for the classical heat equation with a lower
order term.
