  Recently, the error analysis of BDF$k$ $(1\leqslant k\leqslant5)$ SAV (scalar
auxiliary variable) schemes are given in \cite{Huangg:20} for the classical
Allen-Cahn equation. However, it remains unavailable for BDF$6$ SAV schemes. In
this paper, we construct and analyze BDF$6$ SAV schemes for the time-fractional
dissipative systems. We carry out a rigorous error analysis for the
time-fractional Allen-Cahn equation, which also fills up a gap for the
classical case. Finally, numerical experiment is shown to illustrate the
effectiveness of the presented methods. As far as we know, this is the first
SAV schemes for the time-fractional dissipative systems.
