Abstract degenerate Volterra integro-differential equations: inverse generator problem (Q2678441)

The paper is concerned with the inverse generator problem for abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. By inverses of closed multivalued linear operators, the author investigates firstly the problem of generation of exponentially equicontinuous \((a,k)\)-regularized \(C\)-resolvent families and exponentially equicontinuous mild \((a,k)\)-regularized \((C_1,C_2)\)-existence and uniqueness families. The generation of degenerate \(C\)-distribution semigruoups and degenerate \(C\)-distribution cosine functions is then studied. Some applications to abstract degenerate fractional differential equations with Caputo derivatives are finally presented.