(a,k)-Regularized C-Resolvent Families: Regularity and Local Properties

Abstract

We introduce the class of (local) $\left(a,k\right)$-regularized $C$-resolvent families and discuss its basic structural properties. In particular, our analysis covers subjects like regularity, perturbations, duality, spectral properties and subordination principles. We apply our results in the study of the backwards fractional diffusion-wave equation and provide several illustrative examples of differentiable $\left(a,k\right)$-regularized $C$-resolvent families.