Abstract Based on fractional generalized Adams methods, a numerical method is constructed for solving fractional delay differential equations. The convergence of the method is analyzed in detail. The stability of the fractional generalized Adams methods for fractional ordinary differential equations is generalized to a general framework. Under such framework, the linear stability of the method is studied for fractional delay differential equations. Numerical experiments confirm the convergence and the stability of the method.

中文翻译：

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求解分数延迟微分方程的广义 Adams 方法

摘要 基于分数阶广义Adams方法，构造了求解分数阶时滞微分方程的数值方法。详细分析了该方法的收敛性。分数常微分方程的分数广义 Adams 方法的稳定性被推广到一般框架。在此框架下，研究了该方法对分数延迟微分方程的线性稳定性。数值实验证实了该方法的收敛性和稳定性。