Game problems for systems with fractional derivatives of arbitrary order

Abstract

Conflict-controlled processes for systems with Riemann-Liouville derivatives of arbitrary order are studied here. A solution of such a system is presented in the form of a Cauchy formula analog. Using the resolving functions method, sufficient conditions for termination of the game are obtained. These conditions are based on the modified Pontryagin condition, expressed in terms of the generalized matrix functions of Mittag-Leffler. To find the latter, the interpolating polynomial of Lagrange-Sylvester is used. An illustrative example is given.