Work

A Simple Fractional Model with Unusual Dynamics in the Derivative Order

Year: 2025

Type: article

Abstract: Fractional variable order systems with complex dynamics in the order is a little studied topic. In this research, we present three examples of a very simple fractional system with complex dynamics in the order of the derivative. These cases involve different approaches to define the variable order dynamics: 1) an integer-order differential equation that includes the state variable, 2) a differential equation that incorporates the state variable and features both integer and fractional-order derivatives, and 3) fractional variable-order differential equations nested in the orders of the derivatives. We prove a result that shows how the extended recursion of the last case is generalized. These examples illustrate the richness that simple dynamical systems with complex behavior can reveal through the order of their derivatives.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9040264

Authors: Guillermo Fernández-Anaya, Francisco A. Godínez, Rogelio Valdés, Alberto Quezada-Téllez, Marco Polo-Labarrios

Institutions: Universidad Iberoamericana, Universidad Nacional Autónoma de México, Universidad Autónoma del Estado de Hidalgo, Universidad Autónoma Metropolitana

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: Universidad Iberoamericana Ciudad de México