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Spectral approximations to the fractional integral and derivative

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Abstract

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, PR China

    Changpin Li & Fanhai Zeng

  2. School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

    Fawang Liu

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  1. Changpin Li
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  2. Fanhai Zeng
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  3. Fawang Liu
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Correspondence to Changpin Li.

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Li, C., Zeng, F. & Liu, F. Spectral approximations to the fractional integral and derivative. fcaa 15, 383–406 (2012). https://doi.org/10.2478/s13540-012-0028-x

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  • DOI: https://doi.org/10.2478/s13540-012-0028-x

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