Optimal Error Estimates of Spectral Petrov-Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations

We present optimal error estimates for spectral Petrov–Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval. We also develop Laguerre spectral Petrov–Galerkin methods and collocation methods for fractional equations on the half line. Numerical results confirm the error estimates.