An improved collocation method for solving a fractional integro-differential equation

In the paper, an improved collocation method is proposed for solving a linear fractional integro-differential equation. The method is proposed by improving the residual to vanish and require the residual to the minimum in sense of ‖·‖C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Vert \cdot \Vert _C$$\end{document}. It can avoid efficiently ill-conditioned of higher degree polynomials. Convergence order is superconvergence and stability analysis is also provided.