Stability of a Class of Fractional-Order Nonlinear Systems

In this letter stability analysis of fractional order nonlinear systems is studied. Some new sufficient conditions on the local (globally) asymptotic stability for a class of fractional order nonlinear systems with order0<α<2are proposed by using properties of Mittag-Leffler function and the Gronwall inequality. And the corresponding stabilization criteria are also given. The numerical simulations of two systems with order0<α<1and two systems with order1<α<2illustrate the effectiveness and universality of the proposed approach.