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Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator

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  • Farman, Muhammad
  • Sarwar, Rabia
  • Akgul, Ali

Abstract

In this paper, studying a sustainable approach to see the dynamics of infection in the plant by using a fractal fractional derivative. To depict a time-fractional order plant virus model including disease consequences, we suggested a set of fractional differential equations. For the fractional order system, both qualitative and quantitative studies are carried out. To prove the existence and uniqueness of the proposed model with the effect of global derivative, Linear growth and Lipschitz conditions are used. Positiveness and boundedness of solutions of the fractional order model are verified. Local stability analysis and global stability is verified by using the Lyapunov function with the first and second derivative tests. Sensitivity analysis is performed to see the influence of parameters on the fractional order model. To study the effect of the fractional operator, which demonstrates the impact of the illness on plants, solutions are generated with a two-step Lagrange polynomial in the generalized form of the Mittag-Leffler kernel. To observe the behavior of the fractional order plant virus model, numerical simulation is used. Such an inquiry will help to comprehend how the virus behaves and to create defences against infected plants.

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  • Farman, Muhammad & Sarwar, Rabia & Akgul, Ali, 2023. "Modeling and analysis of sustainable approach for dynamics of infections in plant virus with fractal fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002746
    DOI: 10.1016/j.chaos.2023.113373
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    References listed on IDEAS

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    1. Zai-Yin He & Abderrahmane Abbes & Hadi Jahanshahi & Naif D. Alotaibi & Ye Wang, 2022. "Fractional-Order Discrete-Time SIR Epidemic Model with Vaccination: Chaos and Complexity," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Seadawy, Aly R. & Arshad, Muhammad & Lu, Dianchen, 2020. "The weakly nonlinear wave propagation theory for the Kelvin-Helmholtz instability in magnetohydrodynamics flows," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Saima Rashid & Sobia Sultana & Yeliz Karaca & Aasma Khalid & Yu-Ming Chu, 2022. "Some Further Extensions Considering Discrete Proportional Fractional Operators," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-12, February.
    5. Benito Chen-Charpentier, 2022. "Delays in Plant Virus Models and Their Stability," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
    6. Shao-Wen Yao & Aqeel Ahmad & Mustafa Inc & Muhammad Farman & Abdul Ghaffar & Ali Akgul, 2022. "Analysis Of Fractional Order Diarrhea Model Using Fractal Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-12, August.
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    Cited by:

    1. Xu, Changjin & Farman, Muhammad, 2023. "Qualitative and Ulam–Hyres stability analysis of fractional order cancer-immune model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Ma, Zhiying & Hou, Jie & Zhu, Wenhao & Peng, Yaxin & Li, Ying, 2023. "PMNN: Physical model-driven neural network for solving time-fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).

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