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On fractional powers of generators of fractional resolvent families. (English) Zbl 1203.47021
The authors show that if -A generates a bounded α-times resolvent family for some α(0,2], then -A β generates an analytic γ-times resolvent family for β(0,2π-πγ 2π-πα) and γ(0,2). They also derive a generalized subordination principle. In particular, if -A generates a bounded α-times resolvent family for some α(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. 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:
47D06One-parameter semigroups and linear evolution equations
35K90Abstract parabolic equations
47D60C-semigroups, regularized semigroups
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