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.