The paper is devoted to the study of 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 in the case where the Hamiltonian of the equation depends on the time variable in a measurable way. Theorems on the existence and uniqueness of the minimax solution and a theorem on the continuous dependence of this solution on variations of the Hamiltonian and boundary functional are proved. An application of the obtained results to the study of a differential game for a dynamical system described by a differential equation with a Caputo fractional derivative is given.
M. I Gomoyunov (2025) studied this question.