The present paper is an addendum to our recent work on abstract time-fractional equations of the following form: \begin{align}abel{eq0.1} & {\mathbf D}_{t}^{lpha_{n}}u(t)+ umimits_{i=1}^{n-1}A_{i}{\mathbf D}_{t}^{lpha_{i}}u(t)= A{\mathbf D}_{t}^{lpha}u(t)+f(t),\quad t > 0,
& u^{(k)}(0)=u_k,\quad k=0,\cdots, ceil lpha_{n}\rceil -1, \end{align} where $n\in {\mathbb N}\setminus \{1\}$, $A$ and $A_{1},\cdots, A_{n-1}$ are closed linear operators on a sequentiallycomplete locally convex space $X$, $0 eq lpha_{1}<\cdots