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  <doc>
    <id>2230</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1324</pageFirst>
    <pageLast>1360</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>25</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2022-08-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems</title>
    <abstract language="eng">This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-order inhomogeneous linear planar systems and for the Mittag-Leffler stability of an equilibrium point to fractional order nonlinear planar systems. To achieve these goals, our approach is as follows. Firstly, based on Cauchy’s argument principle in complex analysis, we obtain various explicit sufficient conditions for the asymptotic stability of linear systems whose coefficient matrices are constant. Secondly, by using Hankel type contours, we derive some important estimates of special functions arising from a variation of constants formula of solutions to inhomogeneous linear systems. Then, by proposing carefully chosen weighted norms combined with the Banach fixed point theorem for appropriate Banach spaces, we get the desired conclusions. Finally, numerical examples are provided to illustrate the effect of the main theoretical results.</abstract>
    <parentTitle language="eng">Fractional Calculus and Applied Analysis</parentTitle>
    <identifier type="issn">1314-2224</identifier>
    <identifier type="doi">https://doi.org/10.1007/s13540-022-00065-9</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Kai Diethelm</author>
    <author>Ha Duc Thai</author>
    <author>Hoang The Tuan</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-commensurate fractional order planar systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>asymptotic behaviour of solutions</value>
    </subject>
    <collection role="institutes" number="fas">Fakultät Angewandte Sozialwissenschaften</collection>
    <collection role="Regensburger_Klassifikation" number="SA - SP">Mathematik</collection>
    <collection role="ddc" number="515">Analysis</collection>
    <collection role="oa-colour" number="">Gefördert (Hybrid/DEAL)</collection>
    <thesisPublisher>Hochschule für Angewandte Wissenschaften Würzburg-Schweinfurt</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-fhws/files/2230/Diethelm_Asymptotic_behavior.pdf</file>
  </doc>
</export-example>
