IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v152y2012i3d10.1007_s10957-011-9926-z.html
   My bibliography  Save this article

Controllability of Damped Second-Order Impulsive Neutral Functional Differential Systems with Infinite Delay

Author

Listed:
  • G. Arthi

    (Bharathiar University)

  • K. Balachandran

    (Bharathiar University)

Abstract

In this paper, the controllability problem is discussed for the damped second-order impulsive neutral functional differential systems with infinite delay in Banach spaces. Sufficient conditions for controllability results are derived by means of the Sadovskii fixed point theorem combined with a noncompact condition on the cosine family of operators. An example is provided to illustrate the theory.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9926-z
    DOI: 10.1007/s10957-011-9926-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-011-9926-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-011-9926-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. B. Liu, 2004. "Controllability of Neutral Functional Differential and Integrodifferential Inclusions with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 573-593, December.
    2. Y. K. Chang & W. T. Li, 2006. "Controllability of Second-Order Differential and Integro-Differential Inclusions in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 77-87, April.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hamdy M. Ahmed & Mahmoud M. El-Borai & Hassan M. El-Owaidy & Ahmed S. Ghanem, 2019. "Existence Solution and Controllability of Sobolev Type Delay Nonlinear Fractional Integro-Differential System," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
    2. Liang, Jin & Yang, He, 2015. "Controllability of fractional integro-differential evolution equations with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 20-29.
    3. Arthi, G. & Park, Ju H. & Suganya, K., 2019. "Controllability of fractional order damped dynamical systems with distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 74-91.
    4. Eduardo Hernández & Donal O’Regan & Krishnan Balachandran, 2013. "Comments on Some Recent Results on Controllability of Abstract Differential Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 292-295, October.
    5. Elimhan N. Mahmudov, 2018. "Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 345-375, May.
    6. Elimhan N. Mahmudov, 2022. "Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 36-55, January.
    7. Martina Pavlačková & Valentina Taddei, 2022. "Mild Solutions of Second-Order Semilinear Impulsive Differential Inclusions in Banach Spaces," Mathematics, MDPI, vol. 10(4), pages 1-25, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Eduardo Hernández & Donal O’Regan & Krishnan Balachandran, 2013. "Comments on Some Recent Results on Controllability of Abstract Differential Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 292-295, October.
    4. 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.
    5. 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.
    6. Jerzy Klamka, 2020. "Controllability of Semilinear Systems with Multiple Variable Delays in Control," Mathematics, MDPI, vol. 8(11), pages 1-9, November.
    7. Vadivoo, B.Sundara & Raja, R. & Seadawy, R. Aly & Rajchakit, G., 2019. "Nonlinear integro-differential equations with small unknown parameters: A controllability analysis problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 15-26.
    8. 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).
    9. 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.
    10. Elimhan N. Mahmudov, 2018. "Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 345-375, May.
    11. Adisorn Doodee & Anusorn Chonwerayuth, 2022. "Controllability and Hyers-Ulam Stability of Impulsive Integro-differential Equations in Banach Spaces via Iterative Methods," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(4), pages 1-85, November.
    12. Mouffak Benchohra & Fatima Bouazzaoui & Erdal Karapinar & Abdelkrim Salim, 2022. "Controllability of Second Order Functional Random Differential Equations with Delay," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    13. B. Radhakrishnan & K. Balachandran, 2012. "Controllability of Neutral Evolution Integrodifferential Systems with State Dependent Delay," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 85-97, April.
    14. D. Tamizharasan & K. Karthikeyan, 2021. "Controllability results for fractional integrodifferential systems with boundary conditions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 39-45, March.
    15. Elimhan N. Mahmudov, 2022. "Optimization of Higher-Order Differential Inclusions with Special Boundary Value Conditions," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 36-55, January.
    16. Agata Grudzka & Krzysztof Rykaczewski, 2015. "On Approximate Controllability of Functional Impulsive Evolution Inclusions in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 414-439, August.
    17. 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).
    18. 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).
    19. 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).
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9926-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.