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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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