  This paper deals with a two-person zero-sum differential game for a dynamical
system described by a Caputo fractional differential equation of order $\alpha
\in (0, 1)$ 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
$\alpha$ 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.
