Removable Sets for Fractional Heat and Fractional Bessel-Heat Equations

We examine the fractional heat diffusion equations $L_{\gamma ,a}:=(-{\mathrm{\Delta }}_a{)}^{\frac{\gamma }{2}}+{\mathrm{\partial }}_t$, where ${\mathrm{\Delta }}_a$ is the Laplace- or the Bessel-Laplace operator. We give conditions for removability which are sufficient and which are necessary, by $L^p$-capacities. Introducing a spherical modulus of smoothness we can treat the Laplace and Bessel-Laplace cases together.