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Robustness of fractional difference schemes via the Caputo subdiffusion-reaction equations

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  • Owolabi, Kolade M.
  • Atangana, Abdon

Abstract

In this paper, we develop a range of efficient and fast fractional difference schemes for the approximation of Caputo time-fractional subdiffusion-reaction equations. The classical time derivative is replaced with the Caputo fractional derivative operator. The experimental results justify that the numerical solution of the proposed methods compares favourably with the exact solution. Experimental results give a clear indication that dynamical models with non-integer order can yield a better spatial pattern when compared with their classical counterparts.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:111:y:2018:i:c:p:119-127
    DOI: 10.1016/j.chaos.2018.04.019
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    References listed on IDEAS

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    1. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "A new derivative with normal distribution kernel: Theory, methods and applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 476(C), pages 1-14.
    2. Owolabi, Kolade M., 2017. "Mathematical modelling and analysis of two-component system with Caputo fractional derivative order," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 544-554.
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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. & 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.
    3. 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.
    4. 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.
    5. Ma, Wangrong & Jin, Maozhu & Liu, Yifeng & Xu, Xiaobo, 2019. "Empirical analysis of fractional differential equations model for relationship between enterprise management and financial performance," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 17-23.
    6. 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.
    7. 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.
    8. Sene, Ndolane & Abdelmalek, Karima, 2019. "Analysis of the fractional diffusion equations described by Atangana-Baleanu-Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 158-164.
    9. 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.
    10. 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.
    11. Fall, Aliou Niang & Ndiaye, Seydou Nourou & Sene, Ndolane, 2019. "Black–Scholes option pricing equations described by the Caputo generalized fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 108-118.
    12. Ávalos-Ruiz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2018. "FPGA implementation and control of chaotic systems involving the variable-order fractional operator with Mittag–Leffler law," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 177-189.
    13. Sania Qureshi & Norodin A. Rangaig & Dumitru Baleanu, 2019. "New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    14. Maryam Al Owidh & Basma Souayeh & Imran Qasim Memon & Kashif Ali Abro & Huda Alfannakh, 2022. "Heat Transfer and Fluid Circulation of Thermoelectric Fluid through the Fractional Approach Based on Local Kernel," Energies, MDPI, vol. 15(22), pages 1-12, November.
    15. 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.

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