Analysis of the generalized fractional differential system

In this paper, we study the existence, uniqueness, and stability of the solution of the fractional differential system with the generalized fractional derivative. First, the solution of the generalized fractional differential system is obtained by the transformation method. Based on the fixed point theorems, we establish the existing and unique theories of the solution. Furthermore, the sufficient criteria of local stabilities of one-dimensional, two-dimensional, and $ n $ -dimensional linear generalized fractional differential systems are dealt with. In addition, the linearization and stability theorems of the nonlinear generalized fractional differential systems are discussed. Finally, we take the generalized fractional Chen system as an example to illustrate the correctness of the theoretical analysis.