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Numerical solution of the Bagley–Torvik equation using Laguerre polynomials

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Abstract

The Laplace transform and Laguerre polynomials are applied to the solution of the Bagley–Torvik equation. We first convert the fractional differential equation into the algebraic equation by Laplace transform. Then, we find the numerical inversion of Laplace transform by Laguerre polynomials. The fractional derivative is described in the Caputo sense. Numerical examples are provided to demonstrate the accuracy and efficiency of the method.

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Correspondence to Tianfu Ji.

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Ji, T., Hou, J. Numerical solution of the Bagley–Torvik equation using Laguerre polynomials. SeMA 77, 97–106 (2020). https://doi.org/10.1007/s40324-019-00204-y

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Keywords

  • Bagley–Torvik equation
  • Laguerre polynomial
  • Laplace transform
  • Caputo derivative

Mathematics Subject Classification

  • 26A33
  • 34A08
  • 34K28