A Spectral Collocation Method for Nonlinear Fractional Boundary Value Problems with a Caputo Derivative

In this paper, we consider the nonlinear boundary value problems involving the Caputo fractional derivatives of order α∈ (1,2) on the interval (0, T ). We present a Legendre spectral collocation method for the Caputo fractional boundary value problems. We derive the error bounds of the Legendre collocation method under the L^2 - and L^∞ -norms. Numerical experiments are included to illustrate the theoretical results.