On Some Game Problems for First-Order Controlled Evolution Equations

Positional strategies in fractional order differential games

“…An analysis of the scientific literature devoted to positional strategies in differential games of fractional order allows us to conclude that such problems have not been previously studied and it is impossible to transfer the results of well-known works in an obvious way (see [9][10][11][12][13]). Since the differential equation and controlled processes of the fractional order is very different from the usual, integer order.…”

“…To solve the problems considered in this work, the first direct method of L.S. Pontryagin [8][9][10][11][12][13][14][15][16][17][18] is used.…”

The solution of an infinite system of ternary differential equations

“…Thus, there is close relationship between the control problems described by partial differential equations (1) and infinite system of differential equations (3). For example, in [6,7,10,11], differential game problems described by the linear partial differential equation of the next form…”

“…The papers [7,10,11,13,14] suggested studying differential game problems described by infinite system of differential equations (4) in one theoretical frame independently of partial differential equations assuming that λ k , k = 1, 2, . .…”

Pursuit Game for an Infinite System of First-Order Differential Equations with Negative Coefficients

“…This class of differential games occurs naturally as a reformulation for solving controlled distributed systems described by a parabolic equation as in [28] (see also [4,10] for more details). In [29] Satimov and Tukhtasinov study pursuit and evasion problems for controlled equations of the parabolic type. The control parameters occur on the right-hand side of the equations as additive terms.…”