  In this paper, we investigate the inverse generator problem for abstract
degenerate Volterra integro-differential equations in locally convex spaces.
The classes of degenerate $(a,k)$-regularized $C$-resolvent families and
degenerate mild $(a,k)$-regularized $(C_{1},C_{2})$-existence and uniqueness
families play an important role in our analysis. We provide several
illustrative applications of obtained theoretical results, primarily to
abstract degenerate fractional differential equations with Caputo derivatives.
