IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/639801.html
   My bibliography  Save this article

Some Applications of Fractional Calculus in Engineering

Author

Listed:
  • J. A. Tenreiro Machado
  • Manuel F. Silva
  • Ramiro S. Barbosa
  • Isabel S. Jesus
  • Cecília M. Reis
  • Maria G. Marcos
  • Alexandra F. Galhano

Abstract

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.

Suggested Citation

  • J. A. Tenreiro Machado & Manuel F. Silva & Ramiro S. Barbosa & Isabel S. Jesus & Cecília M. Reis & Maria G. Marcos & Alexandra F. Galhano, 2010. "Some Applications of Fractional Calculus in Engineering," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-34, November.
    • Handle: RePEc:hin:jnlmpe:639801
    DOI: 10.1155/2010/639801
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2010/639801.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2010/639801.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2010/639801?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
    ---><---

    Citations

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


    Cited by:

    1. Zaheer Masood & Muhammad Asif Zahoor Raja & Naveed Ishtiaq Chaudhary & Khalid Mehmood Cheema & Ahmad H. Milyani, 2021. "Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems," Mathematics, MDPI, vol. 9(17), pages 1-27, September.
    2. Mohra Zayed & Mahmoud Abul-Ez & Mohamed Abdalla & Nasser Saad, 2020. "On the Fractional Order Rodrigues Formula for the Shifted Legendre-Type Matrix Polynomials," Mathematics, MDPI, vol. 8(1), pages 1-23, January.
    3. Deepika, S. & Veeresha, P., 2023. "Dynamics of chaotic waterwheel model with the asymmetric flow within the frame of Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    4. Gupta, Sandipan & Ranta, Shivani, 2022. "Legendre wavelet based numerical approach for solving a fractional eigenvalue problem," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Panda, Sumati Kumari & Vijayakumar, Velusamy, 2023. "Results on finite time stability of various fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Asjad, Muhammad Imran & Sunthrayuth, Pongsakorn & Ikram, Muhammad Danish & Muhammad, Taseer & Alshomrani, Ali Saleh, 2022. "Analysis of non-singular fractional bioconvection and thermal memory with generalized Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

    More about this item

    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:hin:jnlmpe:639801. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.