中文摘要：

本文利用Jacobi谱配置方法数值求解了一类分数阶多项延迟微分方程，并证明了该方法是收敛的，通过若干数值算例验证了相应的理论结果，结果表明Jacobi谱配置方法求解这类方程是非常高效的，同时也为这类分数阶延迟微分方程的数值求解提供了新的选择，对分数阶泛函方程的数值方法的研究有一定的指导意义．

英文摘要：

In this paper, we study Jacobi spectral collocation method for solving the initial value problem （IVP） of a class of fractional multi-delay differential equations. The convergence of the method for this problem is obtained. Some illustrative examples verify our theoretical results successfully. The results of this paper may provide a new good choice for solving fractional delay differential equations. It is believed that these results will be helpful for the further researches on numerical solutions of fractional functional differential equations.