IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v102y2017icp111-118.html
   My bibliography  Save this article

Impulsive fractional differential equations with Riemann–Liouville derivative and iterative learning control

Author

Listed:
  • Chen, Qian
  • Debbouche, Amar
  • Luo, Zijian
  • Wang, JinRong

Abstract

We try to seek a representation of solution to an initial value problem for impulsive fractional differential equations (IFDEs for short) involving Riemann–Liouvill (RL for short) fractional derivative, then prove an interesting existence result, and introduce Ulam type stability concepts of solution for this kind of equations by introducing some differential inequalities. In addition, we study iterative learning control (ILC for short) problem for system governed by IFDEs via a varying iterative state that does not coincide with a given initial state and apply proportional type learning principle involving the original learning condition to generate each output to following the final path in a finite time interval, then give a convergence result. Numerical examples are reported to check existence and stability of solutions and display the error for different iterative times.

Suggested Citation

  • Chen, Qian & Debbouche, Amar & Luo, Zijian & Wang, JinRong, 2017. "Impulsive fractional differential equations with Riemann–Liouville derivative and iterative learning control," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 111-118.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:111-118
    DOI: 10.1016/j.chaos.2017.03.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917300760
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.03.024?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. Wen-Xue Zhou & Ji-Gen Peng & Yan-Dong Chu, 2012. "Multiple Positive Solutions for Nonlinear Semipositone Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-10, February.
    2. Yan Li & YangQuan Chen & Hyo-Sung Ahn & Guohui Tian, 2013. "A Survey on Fractional-Order Iterative Learning Control," Journal of Optimization Theory and Applications, Springer, vol. 156(1), pages 127-140, January.
    3. Wang, JinRong & Ibrahim, Ahmed Gamal & Fečkan, Michal, 2015. "Nonlocal impulsive fractional differential inclusions with fractional sectorial operators on Banach spaces," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 103-118.
    4. Wen-Xue Zhou & Ying-Xiang Chang & Hai-Zhong Liu, 2012. "Weak Solutions for Nonlinear Fractional Differential Equations in Banach Spaces," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, July.
    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. Suganya, S. & Mallika Arjunan, M. & Trujillo, J.J., 2015. "Existence results for an impulsive fractional integro-differential equation with state-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 54-69.
    2. 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.
    3. 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.
    4. Lin, Zeng & Wang, JinRong & Wei, Wei, 2015. "Fractional differential equation models with pulses and criterion for pest management," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 398-408.
    5. Mohamed Hannabou & Hilal Khalid, 2019. "Investigation of a Mild Solution to Coupled Systems of Impulsive Hybrid Fractional Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2019, pages 1-9, December.
    6. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    7. 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).
    8. Selvaraj Suganya & Mani Mallika Arjunan, 2017. "Existence of Mild Solutions for Impulsive Fractional Integro-Differential Inclusions with State-Dependent Delay," Mathematics, MDPI, vol. 5(1), pages 1-16, January.
    9. Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Yiheng Wei & Bin Du & Songsong Cheng & Yong Wang, 2017. "Fractional Order Systems Time-Optimal Control and Its Application," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 122-138, July.
    11. 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.
    12. 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).
    13. Liu, Shengda & Wang, JinRong & Shen, Dong & O’Regan, Donal, 2019. "Iterative learning control for differential inclusions of parabolic type with noninstantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 48-59.
    14. Arjunan, Mani Mallika & Abdeljawad, Thabet & Anbalagan, Pratap, 2022. "Impulsive effects on fractional order time delayed gene regulatory networks: Asymptotic stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

    More about this item

    Keywords

    IFDEs; Solution; Stability; ILC;
    All these keywords.

    Statistics

    Access and download statistics

    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:102:y:2017:i:c:p:111-118. 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.