具有积分边界条件的非线性耦合分数微分方程组边值问题解的唯一性

Uniqueness of Solutions for Boundary Value Problems of Nonlinear Coupled Fractional Differential Equations with Integral Boundary Conditions

摘要: 分数阶微分方程模型具有深刻的物理背景和丰富的理论内涵，在诸多领域应用广泛，如血液流动问题、化学工程、热弹性、地下水流动、人口动力学等。目前关于带有积分边界条件的非线性耦合分数微分方程边值问题的求解相对较少，本文就是针对非线性耦合分数微分方程边值问题解的唯一性展开的研究，本文的非线性项中含有未知函数的导数项，使得研究的Banach空间更加复杂。首先，得到非线性系统对应的线性系统的Green函数，其次，分析Green函数的性质，构造积分算子，再次，利用Banach不动点定理得到边值问题解的唯一性结果，最后，给出一个示例。

Abstract: Fractional differential equation models have profound physical backgrounds and rich theoretical connotations, and are widely used in many fields, such as blood flow problems, chemical engineer-ing, thermoelasticity, groundwater flow, population dynamics, etc. At present, there is relatively lit-tle research on solving nonlinear coupled fractional differential equation boundary value problems with integral boundary conditions. This paper focuses on the uniqueness of solutions to nonlinear coupled fractional differential equation boundary value problems. The nonlinear term in this paper contains derivative terms of unknown functions, making the Banach studied more complex: Firstly, obtain the Green function of the linear system corresponding to the nonlinear system; secondly, an-alyze the properties of the Green function and construct an integral operator; thirdly, use Banach’s fixed point theorem to obtain the uniqueness result of the solution to the boundary value problem; finally, provide an example.