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Dynamics of multi-pulse splitting process in one-dimensional Gray-Scott system with fractional order operator

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  • Owolabi, Kolade M.
  • Karaagac, Berat

Abstract

In this paper, the dynamic process of pulse-splitting patterns is reported in fractional medium. In the classical Gray-Scott system, the integer-order derivative is replaced with the known Atangana-Baleanu fractional order derivative in the sense of Caputo. mathematical analysis such as the existence of stationary solutions for pulse-splitting process, existence and uniqueness of solutions for the fractional system are presented. The beauty of the work is further demonstrated by presenting numerical results for different values of γ in one dimensional space. We deduced from the numerical experiments that pulse-splitting patterns in both integer and noninteger order scenarios are almost the same.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302356
    DOI: 10.1016/j.chaos.2020.109835
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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. 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.
    6. 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.
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    8. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    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. 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.
    11. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
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    Cited by:

    1. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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