A fractional spectral collocation method for general Caputo two-point boundary value problems

摘要

In this paper we consider a fractional spectral collocation method for solving linear multi-term fractional differential equations involving Caputo-type fractional derivative. By using integral equation method, the boundary value problem of the fractional differential equation is reformulated as an equivalent Volterra-Fredholm integral equation with weakly singular kernels. Then we apply the fractional spectral collocation method to solve the resulting equation. We ensure that the approximate equation has a unique solution and the approximate solution arrives at the optimal convergence order in the infinite norm. At last, numerical examples are given to confirm the theoretical results.