Spectral collocation method for nonlinear Riemann–Liouville fractional differential system

Abstract

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.