ANALYSIS OF FRACTIONAL ORDER DIARRHEA MODEL USING FRACTAL FRACTIONAL OPERATOR

Shao-Wen Yao, Aqeel Ahmad, Mustafa Inc, Muhammad Farman, Abdul Ghaffar and Ali Akgul
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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

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-12

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.

Keywords: Epidemic Model; Lipchitz Function; Ulam–Hyres Stability; Uniqueness; Fractal Fractional Operator (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401739

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