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Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three

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  • Bonab, Zahra Farzaneh
  • Javidi, Mohammad

Abstract

In this paper, a family of explicit methods are presented based on the fractional backward differentiation formula of order three for the numerical solution of the fractional differential equations. The major part of the paper is focused on the study of the stability properties of the introduced methods. The intervals of stability for multistep methods have been calculated and a number of numerical examples are given to confirm theoretical results.

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  • Bonab, Zahra Farzaneh & Javidi, Mohammad, 2020. "Higher order methods for fractional differential equation based on fractional backward differentiation formula of order three," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 71-89.
    • Handle: RePEc:eee:matcom:v:172:y:2020:i:c:p:71-89
    DOI: 10.1016/j.matcom.2019.12.019
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    References listed on IDEAS

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    1. Gholami, Saeid & Babolian, Esmail & Javidi, Mohammad, 2019. "Fractional pseudospectral integration/differentiation matrix and fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 314-327.
    2. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
    3. Galeone, Luciano & Garrappa, Roberto, 2008. "Fractional Adams–Moulton methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1358-1367.
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    Cited by:

    1. Nur Amirah Zabidi & Zanariah Abdul Majid & Adem Kilicman & Faranak Rabiei, 2020. "Numerical Solutions of Fractional Differential Equations by Using Fractional Explicit Adams Method," Mathematics, MDPI, vol. 8(10), pages 1-23, October.

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