Abstract degenerate Volterra integro-differential equations: inverse generator problem

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.