a-times integrated semigroups and fractional derivation

descriptionPublicationkeyboard_double_arrow_right Article 29 Jan 2002Publisher:Walter de Gruyter GmbHJournal:Forum Mathematicum, volume 14 (issn: 0933-7741, eissn: 1435-5337,

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Authors: Miana, Pedro J.;

doi: 10.1515/form.2002.004

a-times integrated semigroups and fractional derivation

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Abstract

The work is devoted to the \(\alpha\)-times integrated semigroups and functional calculus which is related to smooth distribution semigroups. The functional calculus for \(\alpha\)-times integrated semigroups is obtained by applying the fractional integration and derivation to the vector-valued Laplace transform. As application, the fractional powers of the infinitesimal generator, of one \(\alpha\)-times integrated semigroups, are defined.

Keywords

Integrated semigroups, vector-valued Laplace transform, Fractional derivatives and integrals, fractional powers of the infinitesimal generator, \(\alpha\)-times integrated semigroups, smooth distribution semigroups, functional calculus

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