带有瞬时和非瞬时脉冲的分数阶微分方程边值问题的变分结构  

Variational Structure to Boundary Problem of Fractional Differential Equations with Instantaneous and Non-Instantaneous Impulses

作　　者：蔡颖杰 田玉[1] 

机构地区：[1]北京邮电大学,理学院,北京

出　　处：《理论数学》2021年第11期1841-1849,共9页Pure Mathematics

摘　　要：本文首次将瞬时脉冲,非瞬时脉冲和Sturm-Liouville边界条件同时放在分数阶微分方程问题中研究,使用变分法建立了问题的变分结构。此外,由于在同一数学模型中同时考虑瞬时脉冲、非瞬时脉冲和Sturm-Liouville边界条件,我们克服了问题中弱解是经典解的困难。The instantaneous impulsive, non-instantaneous impulsive and Sturm-Liouville boundary condition are studied in the fractional differential equation problem for the first time. The variational structure of problem is established by using the variational method. In addition, considering in-stantaneous impulses condition, non-instantaneous impulses condition and Sturm-Liouville bound-ary condition in the same mathematical model, we overcome the difficulty that the weak solution is the classical solution of problem.

关 键 词：变分法 分数阶微分方程 瞬时脉冲 非瞬时脉冲 Sturm-Liouville边界条件 

分 类 号：O17[理学—数学]