New Constructive Fractional Lyapunov Direct Method for Incommensurate Fractional Order Systems

We address a constructive fractional Lyapunov direct method for Caputo-type incommensurate non-autonomous fractional order systems whenever orders lie in (0,1]. We prove some new fractional Lyapunov theorems by using new ideas of fractional generalized Gronwall inequality and establish higher versions of Lyapunov theorems that give sufficient conditions to predict stability dynamics of equilibrium points of many such systems. We demonstrate the new significance of such a method with five mathematical examples in stability theory.