Convergence analysis of the Jacobi spectral-collocation method for fractional integro-differential equations

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L∞ norm and weighted L2-norm. The numerical examples are given to illustrate the theoretical results.