https://doi.org/10.1140/epjs/s11734-023-00913-6
Regular Article
Optimal synchronization of fractal–fractional differentials on chaotic convection for Newtonian and non-Newtonian fluids
1
Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa
2
Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, Mexico
a
kashif.abro@faculty.muet.edu.pk
c
jose.ga@cenidet.tecnm.mx
Received:
1
February
2023
Accepted:
2
July
2023
Published online:
26
July
2023
A chaotic analysis of thermal convection for non-Newtonian fluid is investigated by employing fractal–fractional differential operators. The most attractive novelty of this investigation is to retrieve the chaotic behavior of non-Newtonian fluid saturated by porosity for the chaotic behavior of Newtonian fluid saturated by porosity. The mathematical modeling of governing equations of non-Newtonian fluid saturated by porosity is constructed in terms of the Caputo–Fabrizio fractal–fractional differential operator subject to the appropriate imposed conditions. For the sake of mathematical analysis, chaotic convection problem of non-Newtonian fluid is explored for dissipation, equilibrium points and criteria of stability. The numerical simulations through Adam–Bashforth method in connection with Caputo–Fabrizio fractal–fractional differential operator are performed for two cases: (1) chaotic convection of non-Newtonian fluid in presence of porosity and (2) chaotic convection of Newtonian fluid in presence of porosity. Finally, the phase portraits have been depicted to identify the similarities and differences among non-Newtonian and Newtonian fluids in presence of porosity.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.