Multiplicative perturbations of local α-times integrated C-semigroups

We establish some left and right multiplicative perturbations of a local α-times integrated C-semigroup S(ċ) on a complex Banach space X with non-densely defined generator, which can be applied to obtain some additive perturbation results concerning S(ċ). Some growth conditions of the perturbations of S(ċ) are also established.