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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
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    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.
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