Abstract degenerate Volterra integro-differential equations: inverse generator problem

Abstract

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.