Study of fractional-order alcohol-abuse mathematical model using the concept of piecewise operator

Muhammad Sher (), Kamal Shah, Muhammad Sarwar (), Bahaaeldin Abdallab () and Thabet Abdeljawad
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Muhammad Sher: Department of Mathematics, University of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan
Kamal Shah: Department of Mathematics, University of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan†Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Muhammad Sarwar: Department of Mathematics, University of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan
Bahaaeldin Abdallab: ��Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Thabet Abdeljawad: ��Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia‡Department of Medical Research, China Medical University, Taichung, Taiwan

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 03, 1-21

Abstract: In this paper, we study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under some advanced concept of fractional derivative called piecewise fractional-order derivative. Currently, most real-world problems are considered under fractional derivatives because of their stable and global behavior. To deal with and detect the crossover behavior in the dynamics of the proposed model, the piecewise derivative containing the Mittag-Leffler-type kernel combined with classical integer order derivatives in piecewise form is used. First, we will investigate the model for qualitative theory in detail. For qualitative theory, we will use fixed point theory. Additionally, we establish sufficient conditions for Ulam–Hyers (UH) stability. To simulate the model, we develop a numerical algorithm based on the Euler technique. The numerical method is applied to present graphically the approximate solutions of the model. In the final part of the paper, we give a detailed discussion of our numerical results.

Keywords: Alcohol-abuse model; piecewise fractional-order derivative; qualitative theory; Euler’s method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500293

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