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

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

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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

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0175.8

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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