分数阶方程组的解与特定分数阶方程的解之间的一个对应关系

A Correspondence between Solutions of a Fractional System and Solutions of a Specific Fractional Equation

摘要: 为了更好地了解下述分数阶方程组 的解的存在性及其性态，其中 ， 是分数阶拉普拉斯算子， 是一个有光滑边界的区域(可以是全空间)且 满足某些特定条件，我们在本文中将证明上述方程组的解与某个特定的分数阶方程的解之间的一个对应关系以便于通过特定的分数阶方程组的解的非存在性、存在性以及唯一性来得到上述方程组的解的非存在性、存在性和唯一性。

Abstract: ITo better understand the existence and behavior of the solution to the following fractional equations where , is the fractional Laplacian operator, is a region with a smooth boundary (which can be a full space) and satisfy some certain conditions. In this paper, we will prove a correspondence between the solutions of the above system and the solutions of a particular fractional equation, which, combining the non-existence, existence, and uniqueness of the solutions of a particular fractional equation, can give out the non-existence, existence and uniqueness of the solutions of the above system.