A stable minimal search method for solving multi-order fractional differential equations based on reproducing kernel space

Abstract

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 e-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.