Abstract Systems of linear Volterra integro-differential equations with convolution type kernels and constant coefficient matrices are considered. It is assumed that the matrix multiplying the higher derivatives of the unknown vector function is singular. A new statement of the initial-value problem different from the conventional statement of a Cauchy problem is considered. Conditions for the solvability of such systems and for the existence and uniqueness of solutions to initial-value problems are obtained. Theoretical results are illustrated by examples.
Chistyakov et al. (2026) studied this question.