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In this paper, we give a novel one-parameter algebraic functional equation for fractional resolvent families. With the help of this functional equation, we are able to show that all fractional resolvent families, except $$C_0$$ C 0 -semigroups, are never exponentially stable.
We show that if −A generates a bounded α-times resolvent family for some α∈(0,2], then −Aβ generates an analytic γ-times resolvent family for β∈(0,2π−πγ2π−πα) and γ∈(0,2). And a generalized subordination principle is derived. In particular, if −A generates a bounded α-times resolvent family for some α∈(1,2], then −A1/α generates an analytic C0-semigroup. Such relations are applied to study the solutions...
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