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We introduce the class of (local) (a,k)-regularized C-resolvent families anddiscuss its basic structural properties. In particular, our analysis covers subjectslike regularity, perturbations, duality, spectral properties and subordinationprinciples. We apply our results in the study of the backwards fractionaldiffusion-wave equation and provide several illustrative examples of differentiable(a,k)-regularized C-resolvent families

abstract and applied analysis

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>-Regularized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math>-Resolvent Families: Regularity and Local Properties

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