Approximate controllability and optimal controls of fractional evolution systems in abstract spaces
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Open access via publisher
Date
2014Type
Journal Article
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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
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School
Department of Mathematics and Statistics
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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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