Memory principle of the Matlab code for Lyapunov Exponents of fractional order

TL;DR

This paper investigates the memory principle in the Matlab code used for calculating Lyapunov exponents of fractional order systems, focusing on impulsive fractional differential equations with different Caputo derivative definitions.

Contribution

It analyzes the memory principle in the Matlab implementation for Lyapunov exponents in fractional systems, providing insights into its behavior with impulsive fractional differential equations.

Findings

Memory principle is confirmed for systems with fixed and changing lower limits.

Numerical examples illustrate the influence of the memory effect.

The analysis clarifies the applicability of the Matlab code to different fractional systems.

Abstract

The paper presents two representative classes of Impulsive Fractional Differential Equations defined with generalized Caputo\'s derivative, with fixed lower limit and changing lower limit, respectively. Memory principle is studied and numerical examples are considered. The problem of the memory principle of the Matlab code for Lyapunov exponents of fractional order systems [Danca & Kuznetsov, 2018] is analyzed.