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

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

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.

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.