Generalized fractional hybrid Hamilton Pontryagin equations

TL;DR

This paper introduces a novel framework combining probabilistic and credibility theories to study generalized fractional hybrid dynamical systems, including new stochastic and fuzzy processes, with applications to Hamilton-Pontryagin equations and numerical simulations.

Contribution

It presents the first formulation of generalized fractional hybrid processes and their application to Hamiltonian systems, integrating stochastic and fuzzy dynamics.

Findings

Derived generalized fractional hybrid Hamilton-Pontryagin equations

Formulated fractional Langevin equations from the hybrid Hamiltonian system

Performed numerical simulations demonstrating the approach's effectiveness

Abstract

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.