Dynamics analysis of the fractional-order Lagrange system

TL;DR

This paper explores the fractional-order Lagrange system using Caputo derivatives, focusing on solution existence, stability, control stabilization, and numerical methods to analyze its dynamic behavior.

Contribution

It introduces a fractional-order model for the Lagrange system and investigates solution properties, stability, control strategies, and numerical integration methods.

Findings

Existence and uniqueness of solutions established.

Asymptotic stability of equilibrium states demonstrated.

Numerical integration via fractional Euler method implemented.

Abstract

The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem, asymptotic stability of its equilibrium states, stabilization problem using appropriate controls and numerical integration via the fractional Euler method.