多项 Caputo 分数阶微分方程 Dirichlet 问题 Lyapunov 型不等式

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1433-1444.

多项 Caputo 分数阶微分方程 Dirichlet 问题 Lyapunov 型不等式

张伟^*(),陈柯元,毋祎,倪晋波

安徽理工大学数学与大数据学院安徽淮南 232001

收稿日期:2024-04-30 修回日期:2024-08-19 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*张伟, E-mail: zhangwei_azyw@163.com
基金资助:
国家自然科学基金(11601007);安徽省自然科学基金资助(2208085-QA05);安徽理工大学大学生创新创业训练计划(202210361102)

Lyapunov-Type Inequalities for Dirichlet Problems of Multi-Term Caputo Fractional Differential Equations

Zhang Wei^*(),Chen Keyuan,Wu Yi,Ni Jinbo

School of Mathematics and Big Data, Anhui University of Science and Technology, Anhui Huainan 232001

Received:2024-04-30 Revised:2024-08-19 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(11601007);Anhui Provincial Natural Science Foundation(2208085-QA05);University Students' Innovation and Pioneering Training Plan Project of Anhui University of Science and Technology(202210361102)

摘要/Abstract

摘要：

该文探讨了一类含参数的多项分数阶微分方程在 Dirichlet 边值条件下的 Lyapunov 型不等式. 首先将分数阶微分方程边值问题等价转化为带 Green 函数的积分方程, 再证明出 Green 函数的相关性质, 最后结合先验估计方法得出相应的 Lyapunov 型不等式. 多项分数阶微分方程属于非局部方程类别, 其复杂性超越了单项分数阶微分方程. 研究多项分数阶微分方程边值问题的 Lyapunov 型不等式, 对定性分析多项分数阶非线性微分方程边值问题具有重要意义.

关键词: 多项分数阶微分方程, Dirichlet 问题, Green 函数, Lyapunov 型不等式

Abstract:

This paper investigates the Lyapunov-type inequalities for a class of multi-term fractional differential equations with with a parameter, subject to Dirichlet boundary conditions. We first transform the fractional boundary value problem into an integral equation with Green's functions, then prove the relevant properties of the Green's functions, and finally obtain the corresponding Lyapunov-type inequalities using a priori estimation method. Multi-term fractional differential equations belong to the category of non-local equations, and their complexity exceeds that of single-term fractional differential equations. Studying the Lyapunov-type inequalities for multi-term fractional boundary value problems is of significant importance for the qualitative analysis of boundary value problems of multi-term fractional nonlinear differential equations.

Key words: Multi-term fractional differential equation, Dirichlet problem, Green's function, Lyapunov-type inequality

中图分类号:

0175.8

张伟, 陈柯元, 毋祎, 倪晋波. 多项 Caputo 分数阶微分方程 Dirichlet 问题 Lyapunov 型不等式[J]. 数学物理学报, 2024, 44(6): 1433-1444.

Zhang Wei, Chen Keyuan, Wu Yi, Ni Jinbo. Lyapunov-Type Inequalities for Dirichlet Problems of Multi-Term Caputo Fractional Differential Equations[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1433-1444.

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