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 the theoretical results obtained primarily to abstract degenerate fractional differential equations with Caputo derivatives.