IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v139y2020ics0960077920304409.html
   My bibliography  Save this article

Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping

Author

Listed:
  • Haq, Abdul
  • Sukavanam, N.

Abstract

This article is concerned with Riemann-Liouville fractional semilinear integrodifferential systems with damping in Banach spaces. First we prove the existence of mild solutions of the system using fixed point approach, then we establish new sufficient conditions for the approximate controllability of the system by means of iterative and approximate technique. To obtain our results, we use the concept of Riemann-Liouville fractional (ϑ, φ, λ) resolvent, where 0 < φ < ϑ ≤ 1 and λ is a real number. Finally, an example is provided for the illustration of the obtained results.

Suggested Citation

  • Haq, Abdul & Sukavanam, N., 2020. "Existence and approximate controllability of Riemann-Liouville fractional integrodifferential systems with damping," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304409
    DOI: 10.1016/j.chaos.2020.110043
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920304409
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110043?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. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.
    2. Chen, Juhn-Horng & Chen, Wei-Ching, 2008. "Chaotic dynamics of the fractionally damped van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 188-198.
    3. Mahmudov, N.I., 2018. "Partial-approximate controllability of nonlocal fractional evolution equations via approximating method," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 227-238.
    4. L. W. Wang, 2009. "Approximate Controllability for Integrodifferential Equations with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 185-206, October.
    5. 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.
    6. Yang, Min & Wang, Qiru, 2016. "Approximate controllability of Riemann–Liouville fractional differential inclusions," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 267-281.
    7. Wang, JinRong & Fĕckan, Michal & Zhou, Yong, 2017. "Center stable manifold for planar fractional damped equations," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 257-269.
    8. Aimene, D. & Baleanu, D. & Seba, D., 2019. "Controllability of semilinear impulsive Atangana-Baleanu fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 51-57.
    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. Malik, Muslim & Vijayakumar, V. & Shukla, Anurag, 2023. "Controllability of discrete-time semilinear Riemann–Liouville-like fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Mohan Raja, M. & Vijayakumar, V., 2022. "Existence results for Caputo fractional mixed Volterra-Fredholm-type integrodifferential inclusions of order r ∈ (1,2) with sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Saha, Kiran Kumar & Sukavanam, N., 2023. "Existence and uniqueness of blow-up solution to a fully fractional thermostat model," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    5. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," 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. Li, Xuemei & Liu, Xinge & Tang, Meilan, 2021. "Approximate controllability of fractional evolution inclusions with damping," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    2. Jiale Sheng & Wei Jiang & Denghao Pang & Sen Wang, 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel," Mathematics, MDPI, vol. 8(12), pages 1-10, December.
    3. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    4. Haq, Abdul, 2022. "Partial-approximate controllability of semi-linear systems involving two Riemann-Liouville fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Haq, Abdul & Sukavanam, N., 2022. "Existence and partial approximate controllability of nonlinear Riemann–Liouville fractional systems of higher order," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    6. Nyamoradi, Nemat & Rodríguez-López, Rosana, 2015. "On boundary value problems for impulsive fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 874-892.
    7. Cao, Yueju & Sun, Jitao, 2017. "Controllability of measure driven evolution systems with nonlocal conditions," Applied Mathematics and Computation, Elsevier, vol. 299(C), pages 119-126.
    8. N. Sukavanam & Surendra Kumar, 2011. "Approximate Controllability of Fractional Order Semilinear Delay Systems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 373-384, November.
    9. 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).
    10. Balasubramaniam, P., 2022. "Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    11. Tian, Xue & Zhang, Yi, 2021. "Fractional time-scales Noether theorem with Caputo Δ derivatives for Hamiltonian systems," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    12. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    13. Yong Zhou & Jia Wei He & Bashir Ahmad & Ahmed Alsaedi, 2018. "Existence and Attractivity for Fractional Evolution Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-9, January.
    14. Kumar, Ashish & Pandey, Dwijendra N., 2020. "Existence of mild solution of Atangana–Baleanu fractional differential equations with non-instantaneous impulses and with non-local conditions," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    15. 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.
    16. Boudjerida, Assia & Seba, Djamila, 2021. "Approximate controllability of hybrid Hilfer fractional differential inclusions with non-instantaneous impulses," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    17. Khan, Hasib & Khan, Aziz & Jarad, Fahd & Shah, Anwar, 2020. "Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    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. Peng, Xiao & Wang, Yijing & Zuo, Zhiqiang, 2022. "Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    20. Zhang, Tao & Lu, Zhong-rong & Liu, Ji-ke & Chen, Yan-mao & Liu, Guang, 2023. "Parameter estimation of linear fractional-order system from laplace domain data," Applied Mathematics and Computation, Elsevier, vol. 438(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:eee:chsofr:v:139:y:2020:i:c:s0960077920304409. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.