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High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology

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  • Owolabi, Kolade M.

Abstract

The concept of fractional derivative has been demonstrated to be successful when applied to model a range of physical and real life phenomena, be it in engineering and science related fields. It is a known fact that reaction-diffusion equation permits the use of different numerical methods in space and time. As a result, we introduce the Fourier spectral method for the discretization of space fractional derivative and adapt the modified version of the exponential time-integrator to advance in time in attempt to explore the dynamic richness of fractional reaction-diffusion equations in two and three dimensions. This approach gives a full diagonal representation of the fractional derivative operator and yields a better spectral convergence irrespective of the value of fractional order chosen in the experiment. Recommendations are made based on some amazing results which arise from the computational experiments. We intend to answer the question ’why is wildlife animals going into extinction in Africa?’ to a reasonable extent. We believe that the spatial patterns obtained in the simulation framework to mimic the ones found in wildlife would provide a measure and serves as a good alternative to an act of killing of wildlife animals for ornamental and decorative purposes, also would serve as a guild to textile industries on pattern formations.

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  • Owolabi, Kolade M., 2020. "High-dimensional spatial patterns in fractional reaction-diffusion system arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301259
    DOI: 10.1016/j.chaos.2020.109723
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    References listed on IDEAS

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    1. 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.
    2. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    3. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    4. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    5. Meerschaert, Mark M. & Mortensen, Jeff & Wheatcraft, Stephen W., 2006. "Fractional vector calculus for fractional advection–dispersion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 181-190.
    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. 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.
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    Citations

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    Cited by:

    1. Owolabi, Kolade M., 2021. "Computational analysis of different Pseudoplatystoma species patterns the Caputo-Fabrizio derivative," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Sweilam, Nasser Hassan & El-Sayed, Adel Abd Elaziz & Boulaaras, Salah, 2021. "Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    4. Alqhtani, Manal & Owolabi, Kolade M. & Saad, Khaled M. & Pindza, Edson, 2022. "Efficient numerical techniques for computing the Riesz fractional-order reaction-diffusion models arising in biology," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Liu, Yue & Lo, Wing-Cheong, 2021. "Deterministic and stochastic analysis for different types of regulations in the spontaneous emergence of cell polarity," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Sarita Kumari & Rajesh K. Pandey & Ravi P. Agarwal, 2023. "High-Order Approximation to Generalized Caputo Derivatives and Generalized Fractional Advection–Diffusion Equations," Mathematics, MDPI, vol. 11(5), pages 1-24, February.
    7. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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