数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 415-426.

• 论文 • 上一篇    下一篇

基于变分法的回火分数阶脉冲微分系统分析

任晶,翟成波*()   

  1. 山西大学数学科学学院 太原 030006
  • 收稿日期:2020-04-29 出版日期:2021-04-26 发布日期:2021-04-29
  • 通讯作者: 翟成波 E-mail:cbzhai@sxu.edu.cn
  • 基金资助:
    山西省自然科学基金(201901D111020);山西省研究生创新项目(2019BY014)

Analysis of Impulsive Tempered Fractional Differential System via Variational Approach

Jing Ren,Chengbo Zhai*()   

  1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
  • Received:2020-04-29 Online:2021-04-26 Published:2021-04-29
  • Contact: Chengbo Zhai E-mail:cbzhai@sxu.edu.cn
  • Supported by:
    the NSF of Shanxi Province(201901D111020);the Graduate Student Innovation Project of Shanxi Province(2019BY014)

摘要:

该文在恰当的容许函数空间中讨论了具有瞬时和非瞬时脉冲的回火分数阶微分方程耦合系统的Dirichlet边值问题.利用变分法得到弱解存在性和唯一性的充分条件,进一步证明了每个弱解都是古典解.最后给出一个实例证明了理论结果的可行性.

关键词: 回火分数阶微分方程, Lax-Milgram定理, 变分法

Abstract:

The aim of this paper is to discuss a Dirichlet boundary value problem for tempered fractional differential system with instantaneous and non-instantaneous impulses in an appropriate admissible function space. By using variational method, we obtain the sufficient condition for the existence and uniqueness of weak solution, moreover, we show that every weak solution is a classical solution. In the end, an example is presented to highlight the feasibility of the theoretical results.

Key words: Tempered fractional differential equation, Lax-Milgram theorem, Variational method

中图分类号: 

  • O175.8