How to construct the fractional dynamical model is one of the most basic problems in fractional dynamics. However, for a long time, a large number of fractional differential equations of motion have been written directly by hand based on integer-order differential equations of motion. In this paper, we establish a new kind of fractional generalized Hamilton equation, and propose a new method to construct the fractional dynamical model, i.e. the fractional generalized Hamilton method with additional terms. As applications of the new method, we construct a series of new fractional dynamical models, which include a family of fractional Micro-electromechanical system (MEMS) with time-varying capacitance, a family of fractional Fokker-Planck model, two kinds of fractional Euler dynamical models of rigid body rotating around a fixed-point, three different kinds of fractional Van der Pol oscillator models and seven different kinds of fractional Duffing oscillator models. The successful construction of these models verifies the effectiveness and actual application value of the fractional generalized Hamilton method with additional terms. The work in this paper is of fundamental significance to the study of fractional dynamics.

如何构建分数阶动力学模型是分数阶动力学中最基本的问题之一。然而，长期以来，大量的分数阶运动微分方程都是基于整数阶运动微分方程直接手工编写的。在本文中，我们建立了一种新的分数式广义Hamilton方程，并提出了一种构建分数式动力学模型的新方法，即带附加项的分数式广义Hamilton方法。作为新方法的应用，我们构建了一系列新的分数动力学模型，其中包括具有时变电容的分数微机电系统（MEMS）族、分数福克-普朗克模型族、两种分数欧拉绕定点旋转的刚体动力学模型，三种不同的分数范德波尔振荡器模型和七种不同的分数达芬振荡器模型。这些模型的成功构建验证了带附加项的分数阶广义Hamilton方法的有效性和实际应用价值。本文的工作对分数动力学的研究具有基础意义。