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Discrete spline methods for solving two point fractional Bagley–Torvik equation

Author

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  • Zahra, W.K.
  • Van Daele, M.

Abstract

A new discrete spline method is developed to solve the two point fractional Bagley–Torvik equation.The method is based on discrete spline function and a nonstandard Grünwald–Letnikov difference (NSGD) and the weighted and shifted Grünwald–Letnikov difference (WSGD) operators to approximate the fractional derivative. Bounds for Grünwald–Letnikov weights are considered. Convergence analysis is discussed and a class of second order and third order methods are obtained. Illustrative examples are presented to validate the practical usefulness of the methods.

Suggested Citation

  • Zahra, W.K. & Van Daele, M., 2017. "Discrete spline methods for solving two point fractional Bagley–Torvik equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 42-56.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:42-56
    DOI: 10.1016/j.amc.2016.09.016
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    Cited by:

    1. Zahra, W.K. & Nasr, M.A. & Van Daele, M., 2019. "Exponentially fitted methods for solving time fractional nonlinear reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 468-490.
    2. Zahra, Waheed K. & Abdel-Aty, Mahmoud & Abidou, Diaa, 2020. "A fractional model for estimating the hole geometry in the laser drilling process of thin metal sheets," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Fathy, Mohamed & Abdelgaber, K.M., 2022. "Approximate solutions for the fractional order quadratic Riccati and Bagley-Torvik differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Muhammed I. Syam & Azza Alsuwaidi & Asia Alneyadi & Safa Al Refai & Sondos Al Khaldi, 2018. "An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem," Mathematics, MDPI, vol. 6(7), pages 1-11, June.

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