We study generalized (in the minimax sense) solutions of a Cauchy problem for a (path-dependent) Hamilton–Jacobi equation with fractional coinvariant derivatives under a right-end boundary condition for the case in which the Hamiltonian of the equation is a measurable function of the time variable. Theorems on the existence and uniqueness of a minimax solution and a theorem on the continuous dependence of this solution on variations in the Hamiltonian and the boundary functional are proved. The results are applied to the study of a differential game for a dynamical system described by a differential equation with a Caputo fractional derivative.
M. I. Gomoyunov (Sat,) studied this question.