一类具p(t)-Laplacian算子的Hadamard分数阶微分方程耦合系统边值问题解的唯一性

Uniqueness of Solutions for Boundary Value Problems of Hadamard Fractional Differential Equation Coupled Systems with p(t)-Laplacian Operator

摘要: 本文研究一类含p(t)-Laplacian算子的Hadamard分数阶微分方程耦合系统非局部边值问题。通过Hadamard分数阶积分与微分的性质，将边值问题转化为等价的积分算子方程；利用Banach压缩映射原理，建立系统解存在唯一的充分条件；构造具体耦合系统实例，通过验证条件及数值计算，证实结论的有效性。研究结果为同类分数阶耦合系统的定性分析提供了新的思路与方法。

Abstract: This paper investigates a class of nonlocal boundary value problems for Hadamard fractional differential equation coupled systems involving the p(t)-Laplacian operator. By virtue of the properties of Hadamard fractional integration and differentiation, the boundary value problem is transformed into an equivalent integral operator equation. Using the Banach contraction mapping principle, sufficient conditions for the existence and uniqueness of solutions to the system are established. A specific example of the coupled system is constructed, and the validity of the conclusions is verified through condition checking and numerical calculation. The research results provide new ideas and methods for the qualitative analysis of similar fractional coupled systems.