Spectral collocation method for solving multi-term fractional integro-differential equations with nonlinear integral

In this paper, we solve the multi-term fractional integro-differential equations with variable coefficients and nonlinear integral using spectral collocation method. We construct a spectral collocation algorithm and provide the rigorous error analysis of our method for the equations with variable coefficients and nonlinear integral. Finally, we give some numerical examples to show the convergence rate and efficiency of the presented method.