IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i1d10.1007_s10957-015-0828-3.html
   My bibliography  Save this article

Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay

Author

Listed:
  • Surendra Kumar

    (University of Delhi)

Abstract

This paper considers fractional optimal control of a semilinear system with fixed delay in a reflexive Banach space. The existence and uniqueness of mild solution are obtained using the Weissinger’s fixed point theorem. The existence of optimal control for the system governed by fractional-order semilinear equation with fixed delay in state is presented. To show the effectiveness of the developed theory, an example is given.

Suggested Citation

  • Surendra Kumar, 2017. "Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 108-121, July.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-015-0828-3
    DOI: 10.1007/s10957-015-0828-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-015-0828-3
    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/s10957-015-0828-3?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. Tian Liang Guo, 2013. "The Necessary Conditions of Fractional Optimal Control in the Sense of Caputo," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 115-126, January.
    2. Jin-Mun Jeong & Sang-Jin Son, 2015. "Time Optimal Control of Semilinear Control Systems Involving Time Delays," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 793-811, June.
    3. JinRong Wang & Michal Fec̆kan & Yong Zhou, 2013. "Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 13-32, January.
    4. JinRong Wang & Yong Zhou & Milan Medveď, 2012. "On the Solvability and Optimal Controls of Fractional Integrodifferential Evolution Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 31-50, January.
    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. Zeng, Yue & Zhang, Yao-jia & Huang, Nan-jing, 2024. "A stochastic fractional differential variational inequality with Lévy jump and its application," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Yang, He & Zhao, Yanxia, 2021. "Existence and optimal controls of non-autonomous impulsive integro-differential evolution equation with nonlocal conditions," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

    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. Rafał Kamocki & Marek Majewski, 2017. "On the Existence and Continuous Dependence on Parameter of Solutions to Some Fractional Dirichlet Problem with Application to Lagrange Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 32-46, July.
    2. Peng, Li & Zhou, Yong & Debbouche, Amar, 2019. "Approximation techniques of optimal control problems for fractional dynamic systems in separable Hilbert spaces," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 234-241.
    3. JinRong Wang & Zhenbin Fan & Yong Zhou, 2012. "Nonlocal Controllability of Semilinear Dynamic Systems with Fractional Derivative in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 292-302, July.
    4. Heydari, M.H. & Hooshmandasl, M.R. & Maalek Ghaini, F.M. & Cattani, C., 2016. "Wavelets method for solving fractional optimal control problems," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 139-154.
    5. shu, Xiao-Bao & Shi, Yajing, 2016. "A study on the mild solution of impulsive fractional evolution equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 465-476.
    6. Surendra Kumar & Shobha Yadav, 2021. "Infinite-delayed stochastic impulsive differential systems with Poisson jumps," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 344-362, June.
    7. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "Stability Analysis and Optimal Control of a Fractional Order Synthetic Drugs Transmission Model," Mathematics, MDPI, vol. 9(7), pages 1-34, March.
    8. Čermák, Jan & Došlá, Zuzana & Kisela, Tomáš, 2017. "Fractional differential equations with a constant delay: Stability and asymptotics of solutions," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 336-350.
    9. Ali Lotfi, 2017. "A Combination of Variational and Penalty Methods for Solving a Class of Fractional Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 65-82, July.
    10. Chongyang Liu & Zhaohua Gong & Changjun Yu & Song Wang & Kok Lay Teo, 2021. "Optimal Control Computation for Nonlinear Fractional Time-Delay Systems with State Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 83-117, October.
    11. Shouguo Zhu & Zhenbin Fan & Gang Li, 2017. "Optimal Controls for Riemann–Liouville Fractional Evolution Systems without Lipschitz Assumption," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 47-64, July.
    12. Yan, Zuomao & Lu, Fangxia, 2017. "Approximate controllability of a multi-valued fractional impulsive stochastic partial integro-differential equation with infinite delay," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 425-447.
    13. Dumitru Baleanu & Amin Jajarmi & Mojtaba Hajipour, 2017. "A New Formulation of the Fractional Optimal Control Problems Involving Mittag–Leffler Nonsingular Kernel," Journal of Optimization Theory and Applications, Springer, vol. 175(3), pages 718-737, December.
    14. Yong Han Kang & Jin-Mun Jeong, 2021. "Time-Optimal Control for Semilinear Stochastic Functional Differential Equations with Delays," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    15. Meghadri Das & Guruprasad Samanta & Manuel De la Sen, 2021. "A Fractional Ordered COVID-19 Model Incorporating Comorbidity and Vaccination," Mathematics, MDPI, vol. 9(21), pages 1-27, November.
    16. Shengda Liu & JinRong Wang, 2017. "Optimal Controls of Systems Governed by Semilinear Fractional Differential Equations with Not Instantaneous Impulses," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 455-473, August.
    17. 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.
    18. JinRong Wang & Michal Fec̆kan & Yong Zhou, 2013. "Relaxed Controls for Nonlinear Fractional Impulsive Evolution Equations," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 13-32, January.
    19. Wang, JinRong, 2015. "Approximate mild solutions of fractional stochastic evolution equations in Hilbert spaces," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 315-323.
    20. Tirumalasetty Chiranjeevi & Raj Kumar Biswas, 2017. "Discrete-Time Fractional Optimal Control," Mathematics, MDPI, vol. 5(2), pages 1-12, April.

    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:174:y:2017:i:1:d:10.1007_s10957-015-0828-3. 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.