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Analysis and numerical simulation of multicomponent system with Atangana–Baleanu fractional derivative

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  • Owolabi, Kolade M.

Abstract

In this paper, we consider the mathematical analysis and numerical simulation of time-fractional multicomponent systems. Here, the classical time derivatives in such systems are replace with the Atangana–Baleanu fractional derivative in the sense of Caputo. This derivative is found useful in the sense that it combines both the non-local and nonsingular kernels in its formulation. A two-step family of Adams–Bashforth method is derived for the approximation of the Atangana–Baleanu derivative. Numerical experiments presented for different instances of α, 0 < α ≤ 1 correspond to our theoretical findings.

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  • Owolabi, Kolade M., 2018. "Analysis and numerical simulation of multicomponent system with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 127-134.
    • Handle: RePEc:eee:chsofr:v:115:y:2018:i:c:p:127-134
    DOI: 10.1016/j.chaos.2018.08.022
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    References listed on IDEAS

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    1. Owolabi, Kolade M. & Atangana, Abdon, 2017. "Analysis and application of new fractional Adams–Bashforth scheme with Caputo–Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 111-119.
    2. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Chaotic behaviour in system of noninteger-order ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 362-370.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Owolabi, Kolade M. & Atangana, Abdon, 2018. "Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 119-127.
    5. Gómez-Aguilar, J.F. & López-López, M.G. & Alvarado-Martínez, V.M. & Reyes-Reyes, J. & Adam-Medina, M., 2016. "Modeling diffusive transport with a fractional derivative without singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 467-481.
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    1. Owolabi, Kolade M., 2019. "Behavioural study of symbiosis dynamics via the Caputo and Atangana–Baleanu fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 89-101.
    2. Owolabi, Kolade M., 2019. "Mathematical modelling and analysis of love dynamics: A fractional approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 849-865.
    3. 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.
    4. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Saad, Khaled M. & Khan, Muhammad Altaf & Agarwal, P., 2019. "Analytic solution for oxygen diffusion from capillary to tissues involving external force effects: A fractional calculus approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 48-65.
    5. Owolabi, Kolade M. & Atangana, Abdon, 2019. "Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 41-49.
    6. Owolabi, Kolade M. & Pindza, Edson, 2019. "Modeling and simulation of nonlinear dynamical system in the frame of nonlocal and non-singular derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 146-157.
    7. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
    8. Karaagac, Berat, 2019. "Two step Adams Bashforth method for time fractional Tricomi equation with non-local and non-singular Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 234-241.
    9. Owolabi, Kolade M. & Karaagac, Berat, 2020. "Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    10. Karaagac, Berat, 2019. "A study on fractional Klein Gordon equation with non-local and non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 218-229.
    11. Abdeljawad, Thabet & Atangana, Abdon & Gómez-Aguilar, J.F. & Jarad, Fahd, 2019. "On a more general fractional integration by parts formulae and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    12. Goufo, Emile F. Doungmo & Khumalo, M & Toudjeu, Ignace Tchangou & Yildirim, Ahmet, 2020. "Mathematical application of a non-local operator in language evolutionary theory," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    13. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    14. Owolabi, Kolade M. & Gómez-Aguilar, J.F. & Karaagac, Berat, 2019. "Modelling, analysis and simulations of some chaotic systems using derivative with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 54-63.

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