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Approximate Controllability of Fractional Order Semilinear Delay Systems

Author

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  • N. Sukavanam

    (IIT Roorkee)

  • Surendra Kumar

    (IIT Roorkee)

Abstract

In this paper, the approximate controllability for a class of semilinear delay control systems of fractional order is proved under the natural assumption that the linear system is approximately controllable. The existence and uniqueness of the mild solution is also proved under suitable assumptions. An example is given to illustrate our main results.

Suggested Citation

  • N. Sukavanam & Surendra Kumar, 2011. "Approximate Controllability of Fractional Order Semilinear Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 373-384, November.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:2:d:10.1007_s10957-011-9905-4
    DOI: 10.1007/s10957-011-9905-4
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    References listed on IDEAS

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    1. L. W. Wang, 2009. "Approximate Controllability for Integrodifferential Equations with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 185-206, October.
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    Cited by:

    1. P. Balasubramaniam & P. Tamilalagan, 2017. "The Solvability and Optimal Controls for Impulsive Fractional Stochastic Integro-Differential Equations via Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 139-155, July.
    2. Daewook Kim & Jin-Mun Jeong, 2021. "Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces," Mathematics, MDPI, vol. 9(6), pages 1-17, March.
    3. Gen Qi Xu, 2023. "Resolvent family for the evolution process with memory," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2626-2656, June.
    4. Ge, Fu-Dong & Zhou, Hua-Cheng & Kou, Chun-Hai, 2016. "Approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 107-120.
    5. 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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    2. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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