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  <doc>
    <id>3226</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>481</pageFirst>
    <pageLast>504</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>34</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Hilbert Space Approach to Fractional Differential Equations</title>
    <abstract language="eng">We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on R, we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.</abstract>
    <parentTitle language="eng">Journal of Dynamics and Differential Equations</parentTitle>
    <identifier type="doi">10.1007/s10884-020-09932-6</identifier>
    <enrichment key="opus.doi.autoCreate">false</enrichment>
    <enrichment key="opus.urn.autoCreate">true</enrichment>
    <author>Kai Diethelm</author>
    <author>Konrad Kitzing</author>
    <author>Rainer Picard</author>
    <author>Stefan Siegmund</author>
    <author>Sascha Trostorff</author>
    <author>Marcus Waurick</author>
    <collection role="institutes" number="fang">Fakultät für angewandte Natur- und Geisteswissenschaften</collection>
  </doc>
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