IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3489-d924001.html
   My bibliography  Save this article

Modified Three-Point Fractional Formulas with Richardson Extrapolation

Author

Listed:
  • Iqbal M. Batiha

    (Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid 2600, Jordan
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates)

  • Shameseddin Alshorm

    (Department of Mathematics, Al Al-Bayt University, Mafraq 25113, Jordan)

  • Adel Ouannas

    (Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria)

  • Shaher Momani

    (Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman 346, United Arab Emirates
    Department of Mathematics, The University of Jordan, Amman 11942, Jordan)

  • Osama Y. Ababneh

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Meaad Albdareen

    (Department of Mathematics, Al Al-Bayt University, Mafraq 25113, Jordan)

Abstract

In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.

Suggested Citation

  • Iqbal M. Batiha & Shameseddin Alshorm & Adel Ouannas & Shaher Momani & Osama Y. Ababneh & Meaad Albdareen, 2022. "Modified Three-Point Fractional Formulas with Richardson Extrapolation," Mathematics, MDPI, vol. 10(19), pages 1-16, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3489-:d:924001
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3489/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/19/3489/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Manuel Duarte Ortigueira & José Tenreiro Machado, 2019. "Fractional Derivatives: The Perspective of System Theory," Mathematics, MDPI, vol. 7(2), pages 1-14, February.
    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. 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. Duarte Valério & Manuel D. Ortigueira, 2023. "Variable-Order Fractional Scale Calculus," Mathematics, MDPI, vol. 11(21), pages 1-13, November.
    3. María Pilar Velasco & David Usero & Salvador Jiménez & Luis Vázquez & José Luis Vázquez-Poletti & Mina Mortazavi, 2020. "About Some Possible Implementations of the Fractional Calculus," Mathematics, MDPI, vol. 8(6), pages 1-22, June.
    4. Duarte Valério & Manuel D. Ortigueira & António M. Lopes, 2022. "How Many Fractional Derivatives Are There?," Mathematics, MDPI, vol. 10(5), pages 1-18, February.

    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:gam:jmathe:v:10:y:2022:i:19:p:3489-:d:924001. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.