Fractional order differential pursuit games with nonlinear controls

The article is devoted to the problems of extending the results and methods of the theory of differential games and optimal control to systems of fractional order. The research is motivated by numerous applications of fractional calculus in control problems of industrial facilities, chemical and biochemical plants, etc. The article considers the problem of pursuit in games represented by nonlinear differential equations of arbitrary fractional order in the sense of Caputo. To study this pursuit problem, we use an approach similar to the method of L. S. Pontryagin, developed for linear differential games of integer orders. In this paper, new sufficient conditions are obtained for solving the pursuit problem in the class of games under study. It has been proven that if these conditions are met, the game can be completed within a certain limited period of time. When solving the pursuit problem, we also used the representation of the solution to a differential equation in terms of generalized matrix functions.