Existence of the solution and stability for a class of variable fractional order differential systems

Abstract

In this paper, the existence results of the solution and stability are focused for the variable fractional order differential equation. In view of the definitions of three kinds of Caputo variable fractional order operator, the sufficient condition of the solution existence for the variable fractional order differential system is obtained by use of Arzela–Ascoli theorem. Moreover, some criterions of the Mittag–Leffler stability and asymptotical stability are proposed for the variable fractional order differential system according to the Fractional Comparison Principle.