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Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives

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  • Ghanbari, Behzad
  • Gómez-Aguilar, J.F.

Abstract

We extended the nutrient–phytoplankton–zooplankton model involving variable-order fractional differential operators of Liouville–Caputo, Caputo–Fabrizio and Atangana–Baleanu. Variable-order fractional operators permits model and describe accurately real world problems, for example, diffusion or spread of nutrients or species in different states. Particularly, we model the interaction of nutrient phytoplankton and its predator zooplankton. The variable-order fractional numerical scheme based on the fundamental theorem of fractional calculus and the Lagrange polynomial interpolation was consider. Numerical simulation results are provided for illustrating the effectiveness and applicability of the algorithm to solve variable-order fractional differential equations.

Suggested Citation

  • Ghanbari, Behzad & Gómez-Aguilar, J.F., 2018. "Modeling the dynamics of nutrient–phytoplankton–zooplankton system with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 114-120.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:114-120
    DOI: 10.1016/j.chaos.2018.09.026
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    1. 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.
    2. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    3. 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.
    4. 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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