分数阶微分方程组边值问题的可解性分析

Solvability analysis of boundary value problems for fractional differential equations

为精准分析分数阶微分方程组边值问题的可解性,提出基于局部稳态融合控制的分数阶微分方程组边值问题的可解性分析方法.首先构建分数阶微分方程组,根据边值分布的非线性奇异扰动特征量,分解其边值融合和向量特征.然后采用光滑边界导向性抑制方法实现对边值柔性暂态跟踪融合,并计算边值问题的可解性的关系参数,将分数阶微分方程组边值问题转化为求线性Robin的边值问题,通过非线性非局部奇异扰动构造分数阶微分方程组的外部解,根据扰动稳态系统的外部解的稳态特征,实现分数阶微分方程组边值问题的可解性分析.最后测试证明得到的分数阶微分方程组边值是稳态收敛的.

In order to accurately analyze the solvability of the boundary value problems,a method based on local steady-state fusion control is proposed to analyze the solvability of the boundary value problems of fractional differential equations.The fractional differential equations are constructed,and the boundary value fusion and vector features are decomposed according to the nonlinear singular perturbation features of the boundary value distribution.The boundary value problem of fractional differential equations is transformed into a linear Robin′s boundary value problem.The external solution of fractional differential equations is constructed by nonlinear nonlocal singular perturbation,and the solvability of the boundary value problem of fractional differential equations is analyzed.The test results show that the boundary value problem of fractional differential equations is stable convergence.