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Entropy
Volume 22
Issue 9
10.3390/e22091027
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Article

Modelling of Chaotic Processes with Caputo Fractional Order Derivative

by
Kolade M. Owolabi
1,2,
José Francisco Gómez-Aguilar
3,*,
G. Fernández-Anaya
4,
J. E. Lavín-Delgado
5 and
E. Hernández-Castillo
6
1
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
2
Department of Mathematical Sciences, Federal University of Technology, Akure PMB 704, Ondo State, Nigeria
3
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca C.P. 62490, Morelos, Mexico
4
Departamento de Física y Matemáticas, Universidad Iberoamericana, CDMX Mexico C.P. 01219, Mexico
5
Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, Cuernavaca C.P. 62490, Morelos, Mexico
6
Instituto Tecnológico de Tlalnepantla, Av. Instituto Tecnológico S/N, Col. La Comunidad, Tlalnepantla de Baz C.P. 54070, Mexico
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(9), 1027; https://doi.org/10.3390/e22091027
Submission received: 31 July 2020 / Revised: 28 August 2020 / Accepted: 31 August 2020 / Published: 14 September 2020
(This article belongs to the Special Issue Fractional Calculus: Application to Chaos and Statistics)
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Abstract

Chaotic dynamical systems are studied in this paper. In the models, integer order time derivatives are replaced with the Caputo fractional order counterparts. A Chebyshev spectral method is presented for the numerical approximation. In each of the systems considered, linear stability analysis is established. A range of chaotic behaviours are obtained at the instances of fractional power which show the evolution of the species in time and space.
Keywords: chaotic dynamics; chebyshev spectral method; fractional differential equation; spatiotemporal oscillations; stability analysis chaotic dynamics; chebyshev spectral method; fractional differential equation; spatiotemporal oscillations; stability analysis

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MDPI and ACS Style

Owolabi, K.M.; Gómez-Aguilar, J.F.; Fernández-Anaya, G.; Lavín-Delgado, J.E.; Hernández-Castillo, E. Modelling of Chaotic Processes with Caputo Fractional Order Derivative. Entropy 2020, 22, 1027. https://doi.org/10.3390/e22091027

AMA Style

Owolabi KM, Gómez-Aguilar JF, Fernández-Anaya G, Lavín-Delgado JE, Hernández-Castillo E. Modelling of Chaotic Processes with Caputo Fractional Order Derivative. Entropy. 2020; 22(9):1027. https://doi.org/10.3390/e22091027

Chicago/Turabian Style

Owolabi, Kolade M., José Francisco Gómez-Aguilar, G. Fernández-Anaya, J. E. Lavín-Delgado, and E. Hernández-Castillo. 2020. "Modelling of Chaotic Processes with Caputo Fractional Order Derivative" Entropy 22, no. 9: 1027. https://doi.org/10.3390/e22091027

APA Style

Owolabi, K. M., Gómez-Aguilar, J. F., Fernández-Anaya, G., Lavín-Delgado, J. E., & Hernández-Castillo, E. (2020). Modelling of Chaotic Processes with Caputo Fractional Order Derivative. Entropy, 22(9), 1027. https://doi.org/10.3390/e22091027

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