Approximation of fractional operators in the frequency domain and its application in chaotic systems

Authors

DOI:

https://doi.org/10.29105/ingenierias28.99-969

Keywords:

Fractional Integrators, Bode diagrams, State Space, Xcos, chaos

Abstract

In this work, a methodology for approximating the fractional-order integrator operator in the frequency domain is considered, based on Bode analysis. This approximation enables the representation of fractional-order systems using integer-order transfer functions, adjusting the fractional order according to the bandwidth and required accuracy. Two ranges of fractional order, [0.1, 0.9] and [0.9, 0.99], are analyzed, verifying that the amplitude diagram slope follows the behavior of −20α dB/decade. Finally, the approximation is implemented in a fractional-order chaotic system, evaluating its effectiveness in generating strange attractors. The results show that the methodology based on Bode diagrams provides an efficient strategy for modeling fractional order chaotic systems within a specific frequency range and its applications in engineering.

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Author Biographies

Ernesto Zambrano-Serrano, Universidad Autonoma de Nuevo Leon

Doctor from IPICYT, Mexico, in 2017. Postdoctoral researcher at BUAP and UANL, and research assistant at City University of Hong Kong. Currently a Professor at FIME-UANL, member of SNI and AMESDYC. His research interests include chaos, complex networks, and fractional systems.

Miguel Ángel Platas-Garza, Universidad Autonoma de Nuevo Leon

Electronics and Automation Engineer from the Universidad Autonoma de Nuevo León (UANL). Subsequently, he received his Master of Science and PhD degrees in Electrical Engineering from the same institution in 2008 and 2011, respectively. Currently works at the Facultad de Ingeniería Mecánica of the UANL as a full professor and head of the Bachelor's degree program in Automation and Intelligent Systems Engineering. Member of the National System of Researchers, the IEEE instrumentation and measurement society, and the Mexican Association of Dynamic Systems and Complexity.

Elizabeth Guadalupe Lara Hernández, Universidad Autonoma de Nuevo Leon

Teacher in Electrical Engineering Sciences with a major in Control from the Universidad Autonoma de Nuevo León (UANL). Works as a full-time professor in Control and Automation, besides being the head of the academy of Power Electronics and Instrumentation in the Facultad de Ingeniería Mecánica y Eléctrica de la UANL.

Efraín Alcorta García, Universidad Autonoma de Nuevo Leon

He holds a Bachelor's and a Master's degree in Engineering from the Universidad Autónoma de Nuevo León (UANL), as well as a Doctorate in Electrical Engineering (Dr.-Ing.) from Gerhard Mercator Universität in Duisburg, Germany (1999). Since 1999, he has been a professor specializing in control systems at the Facultad de Ingeniería Mecánica y Eléctrica (FIME) of UANL. His research interests include automatic control, fault diagnosis, and fault-tolerant control.

Jesús Manuel Muñoz-Pacheco, Benemérita Universidad Autónoma de Puebla,

Doctor of Science from INAOE (2009). He is a research professor at BUAP and has been a member of the National System of Researchers since 2011. Since 2020, he has been included in the Stanford-Elsevier list of the world’s top 2% scientists. He currently serves as an associate editor for JCR-indexed journals. His research interests include cybersecurity and neural networks using chaos theory.

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Portada: Ilustración "Don Quijote a 400 años de Cervantes" Alicia Emárt, Mixta s/papel, 76.5 X 56 cm. Colección de la Biblioteca General del Congreso de la Unión.

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Published

2025-07-30

How to Cite

Zambrano-Serrano, E., Platas-Garza, M. Ángel, Lara Hernández, E. G., Alcorta García, E., & Muñoz-Pacheco, J. M. (2025). Approximation of fractional operators in the frequency domain and its application in chaotic systems. Revista Ingenierías, 28(99), 16–26. https://doi.org/10.29105/ingenierias28.99-969

Issue

Vol. 28 No. 99 (2025): Julio-Diciembre

Section

Artículos

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Copyright (c) 2025 Ernesto Zambrano-Serrano, Miguel Ángel Platas-Garza, Elizabeth Guadalupe Lara Hernández, Efraín Alcorta García, Jesús Manuel Muñoz-Pacheco

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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