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Computational study of multi-species fractional reaction-diffusion system with ABC operator

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  • Owolabi, Kolade M.
  • Atangana, Abdon

Abstract

In this paper, a competition model which describes the spatial interaction among three species in nonlinear fashion is considered. In the model, the standard time derivative is replaced with the Atangana-Baleanu fractional operator in the sense of Caputo. Linear stability analysis which serves as a guide in the choice of parameters when numerically simulating the full system is also examined. The existence and uniqueness of solutions are studied via a fixed point theorem. Different numerical approximation techniques are introduced. Numerical results presented in one and two dimensions revealed some spatiotemporal Turing patterns such as stripes and spots.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:280-289
    DOI: 10.1016/j.chaos.2019.07.050
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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.
    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. Yadav, Swati & Pandey, Rajesh K. & Shukla, Anil K., 2019. "Numerical approximations of Atangana–Baleanu Caputo derivative and its application," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 58-64.
    4. S. Saha Ray & R. K. Bera, 2004. "Solution of an extraordinary differential equation by Adomian decomposition method," Journal of Applied Mathematics, Hindawi, vol. 2004, pages 1-8, January.
    5. 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.
    6. Owolabi, Kolade M., 2016. "Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 89-98.
    7. 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.
    8. 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.
    9. Owolabi, Kolade M., 2018. "Numerical patterns in system of integer and non-integer order derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 143-153.
    10. Saad, Khaled M. & Gómez-Aguilar, J.F., 2018. "Analysis of reaction–diffusion system via a new fractional derivative with non-singular kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 703-716.
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