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

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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.

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Acknowledgements

The author is very grateful to the reviewers for their valuable comments and suggestions.

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  1. Department of Mathematics, Eastern Mediterranean University, Gazimagusa, T.R. North Cyprus, Mersin 10, Turkey

    Nazim I. Mahmudov

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  1. Nazim I. Mahmudov
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Correspondence to Nazim I. Mahmudov.

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Mahmudov, N.I. Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems. J Optim Theory Appl 184, 671–686 (2020). https://doi.org/10.1007/s10957-018-1255-z

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