On the Problem of Pursuing a Group of Coordinated Evadersin a Game with Fractional Derivatives

In a finite-dimensional Euclidean space, we consider the problem of pursuing a group of evaders by a group of pursuers described by a linear nonstationary system of differential equations with fractional Caputo derivatives. The sets of admissible players’ controls—compact sets, terminal sets—the origin of coordinates. Sufficient conditions have been obtained for the capture of at least one evader and all evaders under the condition that the evaders use the same control. In the study, the method of matrix and scalar resolving functions is used as a basic one. It is shown that differential games described by equations with fractional derivatives have properties that are different from those of differential games described by ordinary differential equations.