@Article{NMTMA-10-437,
author = {Changtao Sheng and Jie Shen},
title = {A Hybrid Spectral Element Method for Fractional Two-Point Boundary Value Problems},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2017},
volume = {10},
number = {2},
pages = {437--464},
abstract = {<p style="text-align: justify;">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 $hp$-type error
estimates under $L^2(I)$-norm for the transformed VIEs. Numerical results are provided to show
the effectiveness of the proposed methods.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.s11},
url = {http://global-sci.org/intro/article_detail/nmtma/12353.html}
}