Spectral collocation method for nonlinear Riemann-Liouville fractional differential equations

Abstract

We investigate the spectral collocation method for Riemann-Liouville fractional differential equation (FDE). The main step in the presented method is to transform the FDE to the corresponding nonlinear weakly singular Volterra integral equation (VIE). We provide convergence analysis to show that the presented method has spectral convergency. We carry out numerical experiments to confirm theoretical results.