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

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  • Nazim I. Mahmudov

    (Eastern Mediterranean University, Gazimagusa, T.R. North Cyprus)

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.

Suggested Citation

  • Nazim I. Mahmudov, 2020. "Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 671-686, February.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-018-1255-z
    DOI: 10.1007/s10957-018-1255-z
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    References listed on IDEAS

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    1. R. Ganesh & R. Sakthivel & N. I. Mahmudov & S. M. Anthoni, 2013. "Approximate Controllability of Fractional Integrodifferential Evolution Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, May.
    2. N. I. Mahmudov, 2013. "Approximate Controllability of Fractional Sobolev-Type Evolution Equations in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, March.
    3. Michal Fec̆kan & JinRong Wang & Yong Zhou, 2013. "Controllability of Fractional Functional Evolution Equations of Sobolev Type via Characteristic Solution Operators," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 79-95, January.
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    Cited by:

    1. Sumit Arora & Manil T. Mohan & Jaydev Dabas, 2023. "Finite-Approximate Controllability of Impulsive Fractional Functional Evolution Equations of Order $$1," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 855-890, June.
    2. Mahmudov, N.I., 2020. "Finite-approximate controllability of semilinear fractional stochastic integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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