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 (a, k)-regularized C-resolvent families and mild $$(C_{1},C_{2})$$ -existence uniqueness play an important role our analysis. We provide several illustrative applications theoretical results obtained primarily to fractional differential with Caputo derivatives.