A Hybrid Spectral Element Method for Fractional Two-Point Boundary Value Problems

摘要

We propose a hybrid spectral element method for fractional two-point boundary value problem (FBVPs) involving both Caputo and Riemann-Liouville (RL)fractional derivatives.We first formulate these FBVPs as a second kind Volterra integral equation (VIEs) with weakly singular kernel,following a similar procedure in [16].We then design a hybrid spectral element method with generalized Jacobi functions and Legendre polynomials as basis functions.The use of generalized Jacobi functions allow us to deal with the usual singularity of solutions at t =0.We establish the existence and uniqueness of the numerical solution,and derive a hptype error estimates under L2 (I)-norm for the transformed VIEs.Numerical results are provided to show the effectiveness of the proposed methods.