Spectral approximations to the fractional integral and derivative

• DOI: 10.2478/s13540-012-0028-x
• Publication Date: 2012-06-29T07:16:05Z
• Authors: Changpin Li; Fanhai Zeng; Fawang Liu
• Keywords: Collocation (remote sensing); Derivative (finance); Spectral method

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