IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v434y2022ics0096300322005264.html
   My bibliography  Save this article

Implementation of fractional-order difference via Takenaka-Malmquist functions

Author

Listed:
  • Stanisławski, Rafał
  • Kozioł, Kamil
  • Rydel, Marek

Abstract

The paper presents a new definition of nabla fractional-order difference, equivalent to the Grünwald-Letnikov difference. The difference is based on the general approach of orthonormal basis functions in terms of discrete-time Takenaka-Malmquist filters. The main advantage of the proposed definition is that for finite model length, the model quickly converges to the actual difference. The paper proposes the method of selecting the poles of the Takenaka-Malmquist functions. It also proposes the implementation of the Takenaka-Malmquist-based difference in non-commensurate state-space system and fractional-order integrator. Simulation experiments show the proposed methodology’s high effectiveness in modeling fractional-order difference, integrator, and non-commensurate state-space systems.

Suggested Citation

  • Stanisławski, Rafał & Kozioł, Kamil & Rydel, Marek, 2022. "Implementation of fractional-order difference via Takenaka-Malmquist functions," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    • Handle: RePEc:eee:apmaco:v:434:y:2022:i:c:s0096300322005264
    DOI: 10.1016/j.amc.2022.127452
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005264
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127452?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lu, Xin & Chen, Ning & Li, Hui & Guo, Shiyu & Chen, Zengtao, 2023. "Simulation of the temperature distribution of lithium-ion battery module considering the time-delay effect of the porous electrodes," Energy, Elsevier, vol. 284(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:apmaco:v:434:y:2022:i:c:s0096300322005264. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.