Unique continuation for the fractional heat operator

We study unique continuation properties and the asymptotic behaviour for a class of equations
involving the fractional heat operator with an Hardy-type potential. Our methods are based on
a Almgren-Poon monotonicity formula combined with a blow-up argument. Since the operator
has a global nature we will also need suitable extension results in the spirit of Caffarelli-Silvestre extension.
Key words: Parabolic partial differential equations, unique continuation, blow-up, asymptotics,
monotonicity formula, Hardy potential.