Stochastic generalized fractional HP equations and applications

TL;DR

This paper develops conditions for stochastic generalized fractional Hamilton-Pontryagin equations using Ito calculus, explores their Hamiltonian form, derives Langevin equations, and provides numerical simulations to illustrate their behavior.

Contribution

It introduces stochastic generalized fractional HP equations, establishes their conditions, and connects them to Langevin equations with numerical validation.

Findings

Conditions for stochastic fractional HP equations established

Derived Langevin generalized fractional equations

Numerical simulations demonstrate the equations' behavior

Abstract

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