The spectral collocation method is investigated for the system of nonlinear Riemann–Liouville fractional differential equations (FDEs). The main idea of the presented method is to solve the corresponding system of nonlinear weakly singular Volterra integral equations obtained from the system of FDEs. In order to carry out convergence analysis for the presented method, we investigate the regularity of the solution to the system of FDEs. The provided convergence analysis result shows that the presented method has spectral convergence. Theoretical results are confirmed by numerical experiments. The presented method is applied to solve multi-term nonlinear Riemann–Liouville fractional differential equations and multi-term nonlinear Riemann–Liouville fractional integro-differential equations.

研究了用于非线性Riemann-Liouville分数阶微分方程（FDEs）系统的频谱配置方法。提出的方法的主要思想是求解从FDE系统获得的非线性弱奇异Volterra积分方程组。为了对所提出的方法进行收敛性分析，我们研究了FDEs系统的解的规律性。所提供的收敛性分析结果表明，该方法具有频谱收敛性。理论结果通过数值实验得到证实。所提出的方法适用于求解多项式非线性黎曼– Liouville分数阶微分方程和多项式非线性黎曼– Liouville分数阶积分微分方程。