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An Implicit Hybrid Method for Solving Fractional Bagley-Torvik Boundary Value Problem

Author

Listed:
  • Muhammed I. Syam

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE)

  • Azza Alsuwaidi

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE)

  • Asia Alneyadi

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE)

  • Safa Al Refai

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE)

  • Sondos Al Khaldi

    (Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE)

Abstract

In this article, a modified implicit hybrid method for solving the fractional Bagley-Torvik boundary (BTB) value problem is investigated. This approach is of a higher order. We study the convergence, zero stability, consistency, and region of absolute stability of the modified implicit hybrid method. Three of our numerical examples are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:109-:d:154335
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    References listed on IDEAS

    as
    1. Syam, Muhammed I., 2007. "The modified Broyden-variational method for solving nonlinear elliptic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 392-404.
    2. Karaaslan, Mehmet Fatih & Celiker, Fatih & Kurulay, Muhammet, 2016. "Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 51-58.
    3. 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.
    4. Syam, Muhammed I. & Siyyam, Hani I., 2009. "An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 659-665.
    5. El-Sayed, M.F. & Syam, M.I., 2007. "Numerical study for the electrified instability of viscoelastic cylindrical dielectric fluid film surrounded by a conducting gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 381-400.
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