In this paper, a stable minimal search method based on reproducing kernel space is proposed for solving multi-order fractional differential equations. The existence and uniqueness of solution of the considered equation is proved and the smoothness of the solution is studied. Based on orthonormal bases, we give smooth transformation and a method for obtaining the ε-approximate solution by searching the minimum value. Subsequently, error estimation and stability analysis of the method are obtained. The final several numerical experiments are presented to illustrate the correctness of the theory and the effectiveness of the method.

中文翻译：

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基于再现核空间的多阶分数阶微分方程稳定最小搜索方法

提出了一种基于核空间重构的稳定最小搜索方法求解多阶分数阶微分方程。证明了所考虑方程解的存在性和唯一性，并研究了该解的光滑性。基于正交基，我们提供了平滑变换和一种通过搜索最小值来获得ε-近似解的方法。随后，获得了该方法的误差估计和稳定性分析。最后的几个数值实验表明了该理论的正确性和方法的有效性。