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Volume 6 Issue 3
May  2019

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(3): 760-765
Hossein Aminikhah, Amir Hosein Refahi Sheikhani, Tahereh Houlari and Hadi Rezazadeh, "Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 760-765, May 2019. doi: 10.1109/JAS.2017.7510646
Citation: Hossein Aminikhah, Amir Hosein Refahi Sheikhani, Tahereh Houlari and Hadi Rezazadeh, "Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 760-765, May 2019. doi: 10.1109/JAS.2017.7510646
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Numerical Solution of the Distributed-Order Fractional Bagley-Torvik Equation

doi: 10.1109/JAS.2017.7510646
  • 1.

    Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht 41938-19141, Iran

  • 2.

    Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, Lahijan 1616, Iran

  • 3.

    Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol 46168-49767, Iran, and also with the Department of Applied Mathematics, University of Guilan, Rasht 41938-19141, Iran

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    Abstract
  • In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation. This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributed-order Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the Grunwald-Letnikov method (GLM) and the fractional differential transform method (FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.

     

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