Stochastic Fractional HP Equations

TL;DR

This paper establishes conditions for stochastic fractional Hamilton-Pontryagin equations using Itô calculus, explores their special case for hyperregular Lagrangians, derives Langevin fractional equations, and provides numerical simulations.

Contribution

It introduces new stochastic fractional Hamiltonian equations, derives Langevin fractional equations, and offers numerical validation for these stochastic systems.

Findings

Conditions for stochastic fractional HP equations established

Derived Langevin fractional equations from Hamiltonian systems

Numerical simulations demonstrate the behavior of the equations

Abstract

In this paper we established the condition for a curve to satisfy stochas- tic fractional HP (Hamilton-Pontryagin) equations. These equations are described using It^o integral. We have also considered the case of stochastic fractional Hamiltonian equa- tions, for a hyperregular Lagrange function. From the stochastic fractional Hamiltonian equations, Langevin fractional equations were found and numerical simulations were done.