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    Approximate controllability and optimal controls of fractional evolution systems in abstract spaces

    Access Status
    Open access via publisher
    Authors
    Qin, H.
    Liu, J.
    Zuo, X.
    Liu, Lishan
    Date
    2014
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Qin, H. and Liu, J. and Zuo, X. and Liu, L. 2014. Approximate controllability and optimal controls of fractional evolution systems in abstract spaces. Advances in Difference Equations. 2014 (1).
    Source Title
    Advances in Difference Equations
    DOI
    10.1186/1687-1847-2014-322
    ISSN
    1687-1839
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/62500
    Collection
    • Curtin Research Publications
    Abstract

    © 2014, Qin et al.; licensee Springer.In this paper, under the assumption that the corresponding linear system is approximately controllable, we obtain the approximate controllability of semilinear fractional evolution systems in Hilbert spaces. The approximate controllability results are proved by means of the Hölder inequality, the Banach contraction mapping principle, and the Schauder fixed point theorem. We also discuss the existence of optimal controls for semilinear fractional controlled systems. Finally, an example is also given to illustrate the applications of the main results. MSC:26A33, 49J15, 49K27, 93B05, 93C25.

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