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Optimal synchronization of fractal–fractional differentials on chaotic convection for Newtonian and non-Newtonian fluids

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Abstract

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.

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Acknowledgements

José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014 and SNI-CONACyT.

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Authors and Affiliations

  1. Institute of Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

    Kashif Ali Abro & Abdon Atangana

  2. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Abdon Atangana

  4. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, 62490, Cuernavaca, Morelos, Mexico

    J. F. Gomez-Aguilar

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  1. Kashif Ali Abro
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KAA: conceptualization, methodology, resources, formal analysis, writing—original draft, supervision; AA: conceptualization, methodology, software, writing—original draft preparation; JFG-A: conceptualization, methodology, writing—review editing, validation, final draft preparation, supervision.

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Correspondence to Kashif Ali Abro or J. F. Gomez-Aguilar.

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Abro, K.A., Atangana, A. & Gomez-Aguilar, J.F. Optimal synchronization of fractal–fractional differentials on chaotic convection for Newtonian and non-Newtonian fluids. Eur. Phys. J. Spec. Top. 232, 2403–2414 (2023). https://doi.org/10.1140/epjs/s11734-023-00913-6

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