Spectral approximations to the fractional integral and derivative. (English) Zbl 1276.26016

Summary: 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. A succinct scheme for approximating the Caputo derivative is also derived. A collocation method is proposed to solve the fractional initial value and boundary value problems. Numerical examples are provided to illustrate the effectiveness of the derived methods.


26A33 Fractional derivatives and integrals


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