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

Abstract

In this paper, we consider the nonlinear boundary value problems involving the Caputo fractional derivatives of order \(\alpha \in (1,2)\) 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 \(L^\infty \)-norms. Numerical experiments are included to illustrate the theoretical results.