On viscosity solutions of path-dependent Hamilton–Jacobi–Bellman–Isaacs equations for fractional-order systems

Abstract. This paper deals with a two-person zero-sum differential game for a dynamical system described by a Caputo fractional differential equation of order α ∈ (0, 1) and a Bolza cost functional. The differential game is associated to the Cauchy problem for the path-dependent Hamilton–Jacobi– Bellman–Isaacs equation with so-called fractional coinvariant derivatives of the order α and the corresponding right-end boundary condition. A notion of a viscosity solution of the Cauchy problem is introduced, and the value functional of the differential game is characterized as a unique viscosity solution of this problem.

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