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Analysis Of Fractional Order Diarrhea Model Using Fractal Fractional Operator

Author

Listed:
  • SHAO-WEN YAO

    (School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, P. R. China)

  • AQEEL AHMAD

    (��Department of Mathematics, Ghazi University, Dera Ghazi Khan, Pakistan)

  • MUSTAFA INC

    (��Department of Computer Engineering, Biruni University, Istanbul, Turkey§Department of Medical Research, China Medical University, Taichung, Taiwan)

  • MUHAMMAD FARMAN

    (�Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan)

  • ABDUL GHAFFAR

    (��Department of Mathematics, Ghazi University, Dera Ghazi Khan, Pakistan)

  • ALI AKGUL

    (��Siirt University, Siirt, Turkey)

Abstract

In this paper, we construct a scheme of fractional-order mathematical model for the population infected by diarrhea disease by using the four compartments S, I, T and R. The fractal-fractional derivative operator (FFO) with generalized Mittag-Leffler kernel is employed to obtain the solution of the proposed system. The system is analyzed qualitatively as well as verify non-negative unique solution. The existence and uniqueness results of fractional-order model under Atangana–Baleanu fractal-fractional operator have been proved by fixed point theory. Also error analysis has been made for the proposed fractional-order model. Simulation has been carried out for derived fractional-order scheme to check the effectiveness of the results which will help, how to prevent and control such type of epidemic in society.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401739
    DOI: 10.1142/S0218348X22401739
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    Cited by:

    1. 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).

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