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arXiv · 1005.1725

On fractional powers of generators of fractional resolvent families

Miao Li·Chuang Chen·Fu-Bo Li
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Abstract

We show that if $-A$ generates a bounded $α$-times resolvent family for some $α\in (0,2]$, then $-A^β$ generates an analytic $γ$-times resolvent family for $β\in(0,\frac{2π-πγ}{2π-πα})$ and $γ\in (0,2)$. And a generalized subordination principle is derived. In particular, if $-A$ generates a bounded $α$-times resolvent family for some $α\in (1,2]$, then $-A^{1/α}$ generates an analytic $C_0$-semigroup. Such relations are applied to study the solutions of Cauchy problems of fractional order and first order.

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Miao Li, Chuang Chen, Fu-Bo Li. 2010-07-26. On fractional powers of generators of fractional resolvent families. https://doi.org/10.1016/j.jfa.2010.07.07

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