Linear fractal games of pursuit

Abstract

A general method for solving game problems of pursuit is proposed for dynamical systems with Volterra evolution. The method makes use of resolving functions [1] and the tools of the theory of set-valued mappings. The scheme proposed covers a wide range of functional-differential systems, such as integral, integrodifferential and differential-difference systems of equations defining the dynamics of conflict-controlled processes. A more detailed study is made of game problems for systems with Riemann-Liouville fractional derivatives and regularized Dzhrbashyan-Nersesyan derivatives (“fractal” games). Asymptotic representations of generalized Mittag-Löffler functions are used in the context of the method to establish sufficient conditions for the solvability of game problems.