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Controllability of impulsive functional differential systems with infinite delay in Banach spaces

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  • Chang, Yong-Kui

Abstract

The paper establishes a sufficient condition for the controllability of the first-order impulsive functional differential systems with infinite delay in Banach spaces. We use Schauder’s fixed point theorem combined with a strongly continuous operator semigroup. An example is given to illustrate our results.

Suggested Citation

  • Chang, Yong-Kui, 2007. "Controllability of impulsive functional differential systems with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1601-1609.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:5:p:1601-1609
    DOI: 10.1016/j.chaos.2006.03.006
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    References listed on IDEAS

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    1. Li, Meili & Wang, Miansen & Zhang, Fengqin, 2006. "Controllability of impulsive functional differential systems in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 175-181.
    2. K. Balachandran & J.P. Dauer, 2002. "Controllability of Nonlinear Systems in Banach Spaces: A Survey," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 7-28, October.
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    Cited by:

    1. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "A new approach on approximate controllability of fractional evolution inclusions of order 1 < r < 2 with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Chang, Yong-Kui & Anguraj, A. & Mallika Arjunan, M., 2009. "Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1864-1876.
    3. Hammad, Hasanen A. & Alshehri, Maryam G., 2024. "Application of the Mittag-Leffler kernel in stochastic differential systems for approximating the controllability of nonlocal fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Subalakshmi, R. & Balachandran, K., 2009. "Approximate controllability of nonlinear stochastic impulsive integrodifferential systems in hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2035-2046.
    6. Raja, M. Mohan & Vijayakumar, V. & Udhayakumar, R., 2020. "Results on the existence and controllability of fractional integro-differential system of order 1 < r < 2 via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Y. K. Chang & J. J. Nieto & W. S. Li, 2009. "Controllability of Semilinear Differential Systems with Nonlocal Initial Conditions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 267-273, August.
    8. G. Arthi & K. Balachandran, 2012. "Controllability of Damped Second-Order Impulsive Neutral Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 799-813, March.
    9. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Shukla, Anurag & Nisar, Kottakkaran Sooppy, 2021. "A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order r∈(1,2) with delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    10. Vijayakumar, V. & Udhayakumar, R., 2020. "Results on approximate controllability for non-densely defined Hilfer fractional differential system with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    11. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2021. "A note on the approximate controllability of Sobolev type fractional stochastic integro-differential delay inclusions with order 1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1003-1026.
    12. Cao, Jianxin & Luo, Yiping & Liu, Guanghui, 2016. "Some results for impulsive fractional differential inclusions with infinite delay and sectorial operators in Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 237-257.

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