Spectral approximations to the fractional integral and derivative
Spectral approximations to the fractional integral and derivative
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DOI：
10.2478/s13540-012-0028-x
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发表时间：
2012-09-01
影响因子：
3
通讯作者：
Liu, Fawang
中科院分区：
文献类型：
--
作者：
Li, Changpin;Zeng, Fanhai;Liu, Fawang
本文利用谱近似计算了分数次积分和Caputo导数。基于勒让德多项式、切比雪夫多项式和雅可比多项式，给出了近似分数次积分的有效递推公式。并导出了逼近Caputo导数的简洁格式。提出了求解分数阶初值问题和边值问题的配点法。最后通过数值算例验证了所提出方法的有效性.
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.