期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 15, 期 3, 页码 383-406出版社
SPRINGERNATURE
DOI: 10.2478/s13540-012-0028-x
关键词
fractional integral; Caputo derivative; spectral approximation; Jacobi polynomials
资金
- National Natural Science Foundation of China [10872119]
- Shanghai Leading Academic Discipline Project [S30104]
- Key Program of Shanghai Municipal Education Commission [12ZZ084]
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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