Fractional generalized Hamilton method for equilibrium stability of dynamical systems. (October 2016)

• Record Type: Journal Article
• Authors: Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian
• Is Part Of: Applied mathematics letters. Volume 60(2016:Oct.)
• Page Start: 14
• Page End: 20
• Publication Date: 2016-10
• Subjects: Fractional dynamical system -- Fractional generalized Hamilton method -- Equilibrium stability -- Fractional Duffing oscillator model -- Fractional Whittaker model; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.03.020
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.