Group pursuit in a problem with fractional derivatives in the class of positional strategies with a guide

In a finite-dimensional Euclidean space, the problem of pursuing one evader by a group of pursuers is considered, described by a system of the form
\begin{gather*} D^{(\alpha)} z_i = a_i z_i + u_i - v, u_i, v \in V, \end{gather*}
where $D^{(\alpha)}f$ is the Caputo derivative of order $\alpha\in(0,1)$ of the function $f$. The set of admissible controls $V$ is a convex compact, $a_i$ are non-positive real numbers. The aim of the group of pursuers is to capture the evader. The terminal sets are the origin of coordinates. Sufficient conditions for catching one evader in the class of quasi-strategies are obtained. Using quasi-strategies in an auxiliary game, sufficient conditions for catching an evader in the class of positional strategies with a guide are obtained.