Fractional generalized Hamilton method for equilibrium stability of dynamical systems

In this paper we present a new method for the equilibrium stability of a dynamical system, i.e., the fractional generalized Hamilton method. We reveal the uncertainty and its mathematical representation for the fractional and nonlinear problem and find a general method of constructing a family of fractional dynamical models. And, six criterions of fractional generalized Hamilton method of equilibrium stability are presented. As applications, we explore the equilibrium stability of a fractional Duffing oscillator model and a fractional Whittaker model.