The present paper studies a new class of problems of optimal control theory with second order delay-differential inclusions (DFIs). In the forms of Euler-Lagrange and Hamiltonian type inclusions the sufficient conditions of optimality for delay-DFIs, including the peculiar transversality ones, are proved. In particular, applications of these results to the second order semilinear optimal control problem are illustrated as well as the optimality conditions for nondelayed problems are derived.
Dilara Mastaliyeva (2025) studied this question.