Simple group pursuit with fractional derivatives and integral constraints

This paper addresses the problem of simple pursuit of one evader by a group of pursuers in a differential game described by equations with Caputo fractional derivatives from the interval $(0, 1)$. Integral constraints are imposed on the players' controls, and the pursuers use quasi-strategies. The goal of the group of pursuers is to bring at least one of them within any predetermined distance of the evader. It is proven that if the total energy of the pursuers is greater than the energy of the evader, then the capture occurs in the game.