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\(\alpha\)-times integrated semigroups: local and global. (English) Zbl 1052.47041
The authors investigate the relation between local \(\alpha\)-times integrated semigroups and \((\alpha+1)\)-times integrated Cauchy problems. They also study the relation between global \(\alpha\)-times semigroups and regularized semigroups. Besides, they investigate the well-posedness and mild solutions of the corresponding abstract Cauchy problems and discuss various asymptotic properties of their solutions, such as almost periodicity or Abel-ergodicity.

MSC:
47D62 Integrated semigroups
47D60 \(C\)-semigroups, regularized semigroups
47D03 Groups and semigroups of linear operators
47D06 One-parameter semigroups and linear evolution equations
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