中文摘要：

本文利用三次样条配置方法采用直接法求解一类非线性分数阶比例延迟微分方程初值问题,并得到方法的局部截断误差。通过若干数值算例表明该方法求解分数阶比例延迟微分方程初值问题是非常有效的,本文的结果对于未来研究分数阶比例延迟微分方程的数值方法提供新的思路。

英文摘要：

In this paper,the cubic spline collocation method with two parameters for solving initial value problem（IVPs）of fractional pantograph delay differential equations（FPDDEs）has been discussed.A theorem of the local truncation error is also obtained.Some illustrative examples successfully verify our theoretical results and that the cubic spline collocation method is robust for IVPs of FPDDEs.The obtained works are very helpful for the study of numerical methods for IVPs of FPDDEs.