IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v51y2020i1d10.1007_s13226-020-0387-7.html
   My bibliography  Save this article

Exact Controllability of Multi-Term Time-Fractional Differential System with Sequencing Techniques

Author

Listed:
  • Vikram Singh

    (Indian Institute of Technology Roorkee)

  • Dwijendra N. Pandey

    (Indian Institute of Technology Roorkee)

Abstract

In this paper, an abstract multi-term time-fractional differential system is considered and the existence, uniqueness and exact controllability results are investigated. In this theory, we use the notion of bounded integral contractor introduced by Altman to come up with a new set of sufficient conditions for the exact controllability by constructing a sequencing technique. Moreover, in this technique, we are not required to define induced inverse operator and Lipschitz continuity of nonlinear functions. Finally, an application is given to illustrate the obtained results.

Suggested Citation

  • Vikram Singh & Dwijendra N. Pandey, 2020. "Exact Controllability of Multi-Term Time-Fractional Differential System with Sequencing Techniques," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 105-120, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0387-7
    DOI: 10.1007/s13226-020-0387-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-020-0387-7
    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/s13226-020-0387-7?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. Giona, Massimiliano & Cerbelli, Stefano & Roman, H.Eduardo, 1992. "Fractional diffusion equation and relaxation in complex viscoelastic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 449-453.
    2. Lizzy, R. Mabel & Balachandran, Krishnan & Trujillo, Juan J., 2017. "Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 162-167.
    3. Debbouche, Amar & Antonov, Valery, 2017. "Approximate controllability of semilinear Hilfer fractional differential inclusions with impulsive control inclusion conditions in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 140-148.
    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. 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.
    2. Wei, T. & Li, Y.S., 2018. "Identifying a diffusion coefficient in a time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 77-95.
    3. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    5. Ahmed, Hamdy M. & El-Borai, Mahmoud M., 2018. "Hilfer fractional stochastic integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 182-189.
    6. Yan, Xiong-bin & Zhang, Zheng-qiang & Wei, Ting, 2022. "Simultaneous inversion of a time-dependent potential coefficient and a time source term in a time fractional diffusion-wave equation," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    7. Li, Zhiyuan & Liu, Yikan & Yamamoto, Masahiro, 2015. "Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 381-397.
    8. Sun, Yuting & Hu, Cheng & Yu, Juan & Shi, Tingting, 2023. "Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    9. 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).
    10. Jürgen Geiser & Eulalia Martínez & Jose L. Hueso, 2020. "Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations," Mathematics, MDPI, vol. 8(11), pages 1-42, November.
    11. Chen, Weihao & Liu, Yansheng & Zhao, Daliang, 2024. "Approximate controllability for a class of stochastic impulsive evolution system with infinite delay involving the fractional substantial derivative," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Yongpeng Tai & Ning Chen & Lijin Wang & Zaiyong Feng & Jun Xu, 2020. "A Numerical Method for a System of Fractional Differential-Algebraic Equations Based on Sliding Mode Control," Mathematics, MDPI, vol. 8(7), pages 1-13, July.
    14. 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).

    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:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0387-7. 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.