Stability criterion for a class of nonlinear fractional differential systems

Stability analysis of nonlinear fractional differential systems has been an open problem since the 1990s of the last century. Apparently, Lyapunov’s second method seems to be invalid for nonlinear fractional differential systems (equations). In this paper, we are concerned with this open problem and have solved it partly. Based on Lyapunov’s second method, a novel stability criterion for a class of nonlinear fractional differential system is derived. Our result is simple, global and theoretically rigorous. The conditions to guarantee the stability of the nonlinear fractional differential system are convenient for testing. Compared with the stability criteria in the literature, our criterion is straightforward and suitable for application. Several examples are provided to illustrate the applications of our result.