Persecution of a group of rigidly coordinated evaders in a linear problem with fractional derivatives

In the finite-dimensional Euclidean space, the problem of pursuit of a group of evaders by a pursuit group is considered, which is described by a system of the form
$$D^{(\alpha)} z_{ij} = u_i - v,$$
where $D^{(\alpha)} f$ is the Caputo derivative of order $\alpha \in (0,1)$ of the function $f$. It is assumed that all evaders use the same control. The goal of the pursuers is to catch at least one of the evaders. The goal of the fleeing is to evade the meeting. The evaders use piecewise-program strategies, while the pursuers use piecewise-program counterstrategies. The set of admissible controls is a ball of unit radius with the center at the origin, the target sets being the origin. Sufficient conditions for the capture and sufficient conditions for the evasion are obtained in terms of initial positions and game parameters.