中文摘要：

由于分数阶微分系统具有记忆功能，在其求解过程中计算量较大。文中的目的是针对分数阶Grunwald—Letnikov（GL）定义，研究并寻求一种求解分数阶微分方程的有效数值算法。首先由分数阶GL定义得出分数阶的数值计算公式，进而从理论上分析了算法中分数阶项计算系数的特点，结合计算机数值仿真的结果，得出了远离当前时间的无穷小项一般不可忽略的结论，并设计了一种合理有效的计算方法。计算机数值仿真的结果表明，所设计的求解分数阶微分方程的算法精度高，通用性好，且易于编程实现。

英文摘要：

The calculation work of solving a fractional order differential system is huge since it relating to history. In this brief, for the fractional order dinfinition of Grunwald-Lemikov （ GL）, an effective numerical algorithm for solving fractional order differential systems is investigated. Firstly, the numerical calculation formula of fractional order dinfinition of GL is designed. Secondly, the coefficients of the fractional order term are analyzed theoricaUy, combining with the computer simulation, conclude that the infinitesimal which long away from current can not be omitted. A reasonable effective algorithm is designed well. The results of computer simulation show that the proposed algorithm is a high precision, general one, and it is easy to be programmed.