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Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system

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  • Jena, Rajarama Mohan
  • Chakraverty, Snehashish
  • Jena, Subrat Kumar

Abstract

In this study, the dynamics of the phytoplankton nutrient and whooping cough models have been examined. Mechanisms of transmission of whooping cough and phytoplankton nutrient models are defined in the Atangana-Baleanu-Caputo (ABC) fractional derivative sense. The first biological system is concerned with the dynamics of phytoplankton–nutrient interaction in the recycling of nutrients, and the second is the modeling of whooping cough in the human population. The essential characteristics of the titled models have been presented, and further, the transmissions of the models defined in the ABC sense are addressed. The concept of fixed point theory is used to derive the existence and uniqueness results of the titled models. Solutions are obtained using the homotopy perturbation Elzaki transform method (HPETM), and numerical results are computed. Graphical analysis of the effect of arbitrary order derivatives has been investigated in detail.

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  • Jena, Rajarama Mohan & Chakraverty, Snehashish & Jena, Subrat Kumar, 2020. "Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307670
    DOI: 10.1016/j.chaos.2020.110373
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    References listed on IDEAS

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    1. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2020. "A novel analytical technique for the solution of time-fractional Ivancevic option pricing model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    2. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. 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.
    5. 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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    Cited by:

    1. Jena, Rajarama Mohan & Chakraverty, Snehashish & Baleanu, Dumitru, 2021. "SIR epidemic model of childhood diseases through fractional operators with Mittag-Leffler and exponential kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 514-534.
    2. Jing Chang & Jin Zhang & Ming Cai, 2021. "Series Solutions of High-Dimensional Fractional Differential Equations," Mathematics, MDPI, vol. 9(17), pages 1-21, August.

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