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New concept in calculus: Piecewise differential and integral operators

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  • Atangana, Abdon
  • İğret Araz, Seda

Abstract

In the last decades, many methodologies have been suggested to depict behaviors of some complex world’s problems arising in many academic fields. One of these problems is the multi-steps behavior displayed by some problems. A concept of piecewise derivative is introduced in this paper with the aim to model real world problems following multiples processes. We have presented some important properties of these definitions. We considered different scenarios and presented numerical schemes that could be used to solve such problems. Illustrative examples, including chaotic and epidemiological models are presented to see the effectiveness of the suggested concept.

Suggested Citation

  • Atangana, Abdon & İğret Araz, Seda, 2021. "New concept in calculus: Piecewise differential and integral operators," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077920310298
    DOI: 10.1016/j.chaos.2020.110638
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    1. Naik, Parvaiz Ahmad & Owolabi, Kolade M. & Yavuz, Mehmet & Zu, Jian, 2020. "Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. 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).
    3. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Zhang, Zizhen & Jain, Sonal, 2020. "Mathematical model of Ebola and Covid-19 with fractional differential operators: Non-Markovian process and class for virus pathogen in the environment," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    14. Li, Xiao-Ping & Din, Anwarud & Zeb, Anwar & Kumar, Sunil & Saeed, Tareq, 2022. "The impact of Lévy noise on a stochastic and fractal-fractional Atangana–Baleanu order hepatitis B model under real statistical data," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    15. Silvério Rosa & Faïçal Ndaïrou, 2024. "Optimal Control Applied to Piecewise-Fractional Ebola Model," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    16. Heydari, M.H. & Razzaghi, M., 2021. "A numerical approach for a class of nonlinear optimal control problems with piecewise fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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