α阶右侧Caputo分数阶导数的高阶插值逼近

对α阶(1＜α＜2)右侧Caputo分数阶导数引入新变量以降低函数阶数,采用L2-1插值方法，得到了高阶插值格式。为了进一步改善L2-1方法在区间tN-1，b]上由L1插值带来的非一致O(Δt4-α)阶精度,增加约束条件，使整体区间均利用L2插值得到一致的O(Δt4-α)精度的高阶插值格式,并分别证明了二者的截断误差。

The Higher-Order Interpolation Approximation of the Right Side of Caputo Fractional Derivative

In this paper,a new variable to reduce the order of the function for the fractional derivative of Caputo on the right side of α(1＜α＜2) was introduced,and L2-1 interpolation method was used to obtain the higher order interpolation scheme.In order to further improve the non-uniform O(Δt4-α) order accuracy of L2-1 method on the interval tN-1,b] brought by L1 interpolation,by increasing the constraint conditions,the whole interval was made use of L2 interpolation to obtain the consistent O(Δt4-α) high-order interpolation format,and the truncation errors of both were proved respectively.