Modelling of Chaotic Processes with Caputo Fractional Order Derivative

Kolade M Owolabi; José Francisco Gómez-Aguilar; G Fernández-Anaya; J E Lavín-Delgado; E Hernández-Castillo

doi:10.3390/e22091027

Modelling of Chaotic Processes with Caputo Fractional Order Derivative

Entropy (Basel). 2020 Sep 14;22(9):1027. doi: 10.3390/e22091027.

Authors

Kolade M Owolabi^{1

2}, José Francisco Gómez-Aguilar³, G Fernández-Anaya⁴, J E Lavín-Delgado⁵, E Hernández-Castillo⁶

Affiliations

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.

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.