Matrix Resolving Functions in the Linear Group Pursuit Problem With Fractional Derivatives

Abstract

In finite-dimensional Euclidean space, we analyze the problem of pursuit of a single evader by a group of pursuers, which is described by a system of differential equations with Caputo fractional derivatives of order \(alpha.\) The goal of the group of pursuers is the capture of the evader by at least \(m\) different pursuers (the instants of capture may or may not coincide). As a mathematical basis, we use matrix resolving functions that are generalizations of scalar resolving functions. We obtain sufficient conditions for multiple capture of a single evader in the class of quasi-strategies. We give examples illustrating the results obtained.