中山大学学报（自然科学版）2018，Vol.57Issue(1)：55-62,8.DOI:10.13471/j.cnki.acta.snus.2018.01.008
带非线性延迟项的分数阶微分积分方程收敛性
Convergence analysis for fractional integral and differential equation with nonlinear delay
摘要
Abstract
The fractional integral and differential equation with nonlinear delay is studied with Jacobi spectral-collocation method.After proper linear transformation,an approximate solution and an approxi-mate derivative of the solution are obtained by Gauss quadrature formula.By Jacobi collocation discretiza-tion,a rigorous error analysis is provided to show that the error of the approximate solution and the error of the approximate derivative both decay exponentially in the infinity norm and the weighted L2-norm.关键词
Jacobi谱配置方法/非线性延迟项/分数阶导数/微分积分方程/高斯求积公式/收敛分析Key words
Jacobi spectral-collocation method/nonlinear delay/fractional derivative/the fractional in-tegral and differential equation/Gauss quadrature formula/convergence analysis分类
数理科学引用本文复制引用
郑伟珊..带非线性延迟项的分数阶微分积分方程收敛性[J].中山大学学报（自然科学版）,2018,57(1):55-62,8.基金项目
国家自然科学基金(11626074) （11626074）
韩山师范学院项目(201404, Z16027, 2017HJGJCJY009) （201404, Z16027, 2017HJGJCJY009）
