# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On fractional powers of generators of fractional resolvent families. (English) Zbl 1203.47021
The authors show that if $-A$ generates a bounded $\alpha$-times resolvent family for some $\alpha \in \left(0,2\right]$, then $-{A}^{\beta }$ generates an analytic $\gamma$-times resolvent family for $\beta \in \left(0,\frac{2\pi -\pi \gamma }{2\pi -\pi \alpha }\right)$ and $\gamma \in \left(0,2\right)$. They also derive a generalized subordination principle. In particular, if $-A$ generates a bounded $\alpha$-times resolvent family for some $\alpha \in \left(1,2\right]$, then $-{A}^{1/\alpha }$ generates an analytic ${C}_{0}$-semigroup. Such relations are applied to study the solutions of Cauchy problems of fractional order and first order. These results allow to the authors to give a unitary perspective to the variegate phenomena related to fractional operators and to establish a connection between solutions of fractional Cauchy problems and Cauchy problems of first order.
##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 35K90 Abstract parabolic equations 47D60 $C$-semigroups, regularized semigroups