IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v4y2016i4p60-d80841.html
   My bibliography  Save this article

A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces

Author

Listed:
  • Dimplekumar Chalishajar

    (Department of Applied Mathematics, 435 Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450, USA)

  • Annamalai Anguraj

    (Department of Mathematics, PSG College of Arts and Science, Coimbatore, Tamil Nadu 641014, India)

  • Kandasamy Malar

    (Department of Mathematics, Erode Arts and Science College, Erode, Tamil Nadu 638009, India)

  • Kulandhivel Karthikeyan

    (Department of Mathematics, K.S.R. College of Technology, Tiruchengode, Tamil Nadu 637215, India)

Abstract

In this paper, we study the problem of controllability of impulsive neutral evolution integro-differential equations with state-dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii’s fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

Suggested Citation

  • Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:4:p:60-:d:80841
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/4/4/60/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/4/4/60/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. B. Radhakrishnan & K. Balachandran, 2011. "Controllability Results for Second Order Neutral Impulsive Integrodifferential Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 589-612, December.
    2. Dimplekumar N. Chalishajar, 2012. "Controllability of Second Order Impulsive Neutral Functional Differential Inclusions with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 672-684, August.
    3. X. Zhang, 2000. "Exact Controllability of Semilinear Evolution Systems and Its Application," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 415-432, November.
    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. Balasubramaniam, P. & Tamilalagan, P., 2015. "Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi’s function," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 232-246.
    6. Xuetao Yang & Quanxin Zhu & Zhangsong Yao, 2014. "p th Moment Exponential Stability of Nonlinear Hybrid Stochastic Heat Equations," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-7, August.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Nazim Mahmudov, 2013. "Exact null controllability of semilinear evolution systems," Journal of Global Optimization, Springer, vol. 56(2), pages 317-326, June.
    3. Jerzy Klamka, 2020. "Controllability of Semilinear Systems with Multiple Variable Delays in Control," Mathematics, MDPI, vol. 8(11), pages 1-9, November.
    4. 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.
    5. Tajani, Asmae & El Alaoui, Fatima-Zahrae & Boutoulout, Ali, 2022. "Regional boundary controllability of semilinear subdiffusion Caputo fractional systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 481-496.
    6. 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.
    7. 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.
    8. Lu, Liang & Liu, Zhenhai & Bin, Maojun, 2016. "Approximate controllability for stochastic evolution inclusions of Clarke’s subdifferential type," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 201-212.
    9. 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.
    10. 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.
    11. Jia Wei He & Yong Liang & Bashir Ahmad & Yong Zhou, 2019. "Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)," Mathematics, MDPI, vol. 7(2), pages 1-17, February.
    12. 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.
    13. 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.
    14. 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.
    15. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    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. Lu, Liang & Liu, Zhenhai, 2015. "Existence and controllability results for stochastic fractional evolution hemivariational inequalities," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1164-1176.
    18. Dimplekumar N. Chalishajar & Kulandhivel Karthikeyan & Annamalai Anguraj, 2016. "Existence of Semi Linear Impulsive Neutral Evolution Inclusions with Infinite Delay in Frechet Spaces," Mathematics, MDPI, vol. 4(2), pages 1-17, April.
    19. Shukla, Anurag & Vijayakumar, V. & Nisar, Kottakkaran Sooppy, 2022. "A new exploration on the existence and approximate controllability for fractional semilinear impulsive control systems of order r∈(1,2)," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    20. 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.

    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:gam:jmathe:v:4:y:2016:i:4:p:60-:d:80841. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.