分数因子与分数阶完整力学系统的运动方程和循环积分

引入分数因子和分数增量，给出了分数阶微积分的定义和性质；基于分数阶导数的定义，证明了含有分数因子的等时变分与分数阶算子的交换关系；提出了分数阶完整保守和非保守系统的Hamilton原理；建立了分数阶完整保守系统和非保守系统的运动微分方程；得到了分数阶完整保守系统的循环积分；并利用分数阶循环积分导出分数阶罗兹方程．最后给出了两个例子．研究表明利用分数因子给出的分数阶微分方程是一个含有分数因子的通常的微分方程，那么分数阶系统运动微分方程的求解都可以采用通常微分方程的求解方法．

Fractional Motion Equations and Circulatory Integrals of Holonomic Dynamical Systems with Fractional Gene

Firstly, a fractional gene and a fractional increment are put forward and the definitions and properties of fractional derivative and integral with fractional gene are given. Secondly, the exchanging relationship between the isochronous variation and fractional derivative with the fractional gene is proved. Thirdly, the fractional Hamilton principles and fractional differential equations with fractional gene for holonomic dynamical systems are presented. Further, the fractional circulatory integrals of the systems are obtained and the fractional Routh’s equations with fractional gene are derived. Finally, two examples are given. This research indicates that the fractional differential equations can become the conventional differential equations with fractional gene, and the general methods for solving the conventional differential equations are also applicable for solving the fractional differential equations.