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Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative

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  • Owolabi, Kolade M.
  • Hammouch, Zakia

Abstract

In this paper, a robust numerical simulation technique based on the fractional Adams–Bashforth and the Fourier spectral methods are formulated to explore some spatiotemporal patterns in a range of Belousov–Zhabotinskii reaction systems. The standard integer-order time-derivative is replaced with the Atangana–Baleanu fractional order derivative in the sense of Caputo. Details of existence and stability of positive solution are given. Numerical experiments are carried out at some instances of fractional power α to demonstrate the suitability of the methods, and to explore the dynamic richness in some chemical species when modelled with non-integer-order derivatives.

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  • Owolabi, Kolade M. & Hammouch, Zakia, 2019. "Spatiotemporal patterns in the Belousov–Zhabotinskii reaction systems with Atangana–Baleanu fractional order derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1072-1090.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:1072-1090
    DOI: 10.1016/j.physa.2019.04.017
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    References listed on IDEAS

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    1. Owolabi, Kolade M., 2018. "Numerical patterns in reaction–diffusion system with the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 160-169.
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    5. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
    6. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
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    Cited by:

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    3. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Al-khedhairi, A. & Elsadany, A.A. & Elsonbaty, A., 2019. "Modelling immune systems based on Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 25-39.
    5. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    6. Qureshi, Sania & Aziz, Shaheen, 2020. "Fractional modeling for a chemical kinetic reaction in a batch reactor via nonlocal operator with power law kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    7. Tajadodi, H., 2020. "A Numerical approach of fractional advection-diffusion equation with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. Ghalib, M. Mansha & Zafar, Azhar A. & Riaz, M. Bilal & Hammouch, Z. & Shabbir, Khurram, 2020. "Analytical approach for the steady MHD conjugate viscous fluid flow in a porous medium with nonsingular fractional derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    9. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    10. Asif, Muhammad & Ali Khan, Zar & Haider, Nadeem & Al-Mdallal, Qasem, 2020. "Numerical simulation for solution of SEIR models by meshless and finite difference methods," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    11. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Computational study of multi-species fractional reaction-diffusion system with ABC operator," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 280-289.
    12. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    13. Naik, Parvaiz Ahmad & Zu, Jian & Owolabi, Kolade M., 2020. "Global dynamics of a fractional order model for the transmission of HIV epidemic with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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