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Modeling and analysis of the polluted lakes system with various fractional approaches

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  • El-Dessoky Ahmed, M.M.
  • Altaf Khan, Muhammad

Abstract

The purpose of this paper is to investigate the dynamics of the polluted lakes system through fractional derivative approach in the sense of fractal-fractional operator. Initially, we derive the model based on the assumptions and then apply the fractal-fractional operator. The model with fractal-fractional approach in the sense of Atangana–Baleanu derivative is considered. When, choosing the fractal order one we obtain fractional order, and when choosing the fractional order one a fractal system is obtained. Considering both the operators together we present a model with fractal-fractional. We present a novel numerical approach to solve the fractal-fractional system and then present the existence and uniqueness results for the system. We present various graphical results for the fractal and fractional operators and also for the fractal-fractional orders. The graphical results reveals the significance of the new operator to a practical problem in a better way.

Suggested Citation

  • El-Dessoky Ahmed, M.M. & Altaf Khan, Muhammad, 2020. "Modeling and analysis of the polluted lakes system with various fractional approaches," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301223
    DOI: 10.1016/j.chaos.2020.109720
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    References listed on IDEAS

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    1. Arqub, Omar Abu & Maayah, Banan, 2018. "Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 117-124.
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    Cited by:

    1. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. 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).
    3. Higazy, M., 2020. "Novel fractional order SIDARTHE mathematical model of COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).

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