Stability analysis of fractional-order differential equations with multiple delays: The [formula omitted] case

Abstract

In this paper, the asymptotic stability of nonlinear fractional-order differential equations with multiple delays under the Caputo’s fractional derivative with 1<α<2 is considered. Compared with the existing literature about fractional-order differential equations with 1<α<2, time delays are taken into consideration at the first time. By using the Laplace transform method and root locus technique, a necessary and sufficient condition is given in a coefficient-type criterion to ensure the asymptotic stability of fractional-order differential equations with multiple delays. The coefficient-type criterion is formulated by the coefficients and fractional exponent, which is easily verified in practical applications. Eventually, numerical examples are offered to show the effectiveness and feasibility of the main results.