Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems

Nazim I. Mahmudov ()
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Nazim I. Mahmudov: Eastern Mediterranean University, Gazimagusa, T.R. North Cyprus

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 2, No 18, 686 pages

Abstract: Abstract In this work, we extend a variational approach to study the finite-approximate controllability for Sobolev-type fractional semilinear evolution equations with nonlocal conditions in Hilbert spaces. Assuming the approximate controllability of the corresponding linear equation, we obtain sufficient conditions for the finite-approximate controllability of the Sobolev-type fractional system. We prove that, with one sole control, one can obtain simultaneously approximate controllability and exact reachability of a finite number of constraints. The obtained result is a generalization and continuation of the recent results on this issue. An example is given as an application of our result.

Keywords: Finite-approximate controllability; Fractional evolution systems; Nonlocal conditions; Gramian controllability operator; Mittag–Leffler functions; 47J35; 93B05; 93C25 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-018-1255-z

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