广义分数阶混杂Hamilton Pontryagin方程
Generalized fractional hybrid Hamilton Pontryagin equations
摘要：
在这项工作中，我们提出了一个新的方法来研究动力系统。结合不确定性的两种表达方式，利用概率论和可信性理论，研究了广义分数阶混合方程。本文引入了广义分数Wiener过程、广义分数Liu过程以及两者的组合广义分数混合过程的概念。相应的广义分数随机，模糊，混合动力系统的定义。我们将理论应用于广义分数阶混合Hamilton-Pontryagin（HP）方程、广义分数阶Hamilton方程。从一般的分数阶混合哈密顿方程出发，建立了分数阶朗之万方程，并进行了数值模拟。
英文摘要：
In this work we present a new approach on studying dynamical systems. Combining the two ways of expressing the uncertainty, using probabilistic theory and credibility theory, we have research the generalized fractional hybrid equations. We have introduced the concepts of generalized fractional Wiener process, generalized fractional Liu process and the combination between those two, generalized fractional hybrid process. Corresponding generalized fractional stochastic, respectively fuzzy, respectively hybrid dynamical systems were defined. We applied the theory for generalized fractional hybrid Hamilton-Pontryagin (HP) equation, generalized fractional Hamiltonian equations. From the general fractional hybrid Hamiltonian equations, fractional Langevin equations were found and numerical simulations were done.
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