基于Chebyshev多项式逼近，建立关于分数阶积分与Caputo型分数阶微分的数值算法.对分数阶积分提出新的计算格式,对Caputo型分数阶微分则推广了原有的数值方法,并分别给出相应的误差估计.最后,通过数值例子说明了构造算法的有效性.

Numerical algorithms based on Chebyshev polynomial approximation are proposed, including a numerical algorithm for fractional integral and a generalized numerical algorithm for fractional derivative. Error estimates are given. Numerical examples show effectiveness of the methods.