An hp-version Legendre spectral collocation method for multi-order fractional differential equations

Abstract

In this paper, we consider the multi-order fractional differential equation and recast it into an integral equation. Based on the integral equation, we develop an hp-version Legendre spectral collocation method and the integral terms with the weakly singular kernels are calculated precisely according to the properties of Legendre and Jacobi polynomials. The hp-version error bounds under the L2-norm and the $L^{\infty }$ -norm are derived rigorously. Numerical experiments are included to illustrate the efficiency of the proposed method and the rationality of the theoretical results.