标题： 分数阶经典力学 显示英文标题

标题： Fractional Classical Mechanics

摘要： 分数经典力学作为分数量子力学的经典对应被引入和开发。 已经为分数经典力学实现了拉格朗日、哈密顿和哈密顿-雅可比框架。 已经引入了分数经典力学的拉格朗日量，并得到了运动方程。 分数振子模型在1D情况下被提出并求解。 已经发现了分数经典振子振动周期的新方程。 讨论了经典振子周期的能量依赖性与分数量子振子能量级非等距分布之间的相互作用。 我们还讨论了分数经典力学的新方程与经典力学中著名基本方程之间的关系。 显示英文摘要

摘要： Fractional classical mechanics has been introduced and developed as a classical counterpart of the fractional quantum mechanics. Lagrange, Hamilton and Hamilton-Jacobi frameworks have been implemented for the fractional classical mechanics. The Lagrangian of fractional classical mechanics has been introduced, and equation of motion has been obtained. Fractional oscillator model has been launched and solved in 1D case. A new equation for the period of oscillations of fractional classical oscillator has been found. The interplay between the energy dependency of the period of classical oscillations and the non-equidistant distribution of the energy levels for fractional quantum oscillator has been discussed. We discuss as well, the relationships between new equations of fractional classical mechanics and the well-known fundamental equations of classical mechanics.