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- Title
Study of fractional-order alcohol-abuse mathematical model using the concept of piecewise operator.
- Authors
Sher, Muhammad; Shah, Kamal; Sarwar, Muhammad; Abdallab, Bahaaeldin; Abdeljawad, Thabet
- 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.
- Subjects
FIXED point theory; MATHEMATICAL models; ALCOHOL drinking; MODEL theory; EULER method
- Publication
International Journal of Modern Physics C: Computational Physics & Physical Computation, 2024, Vol 35, Issue 3, p1
- ISSN
0129-1831
- Publication type
Article
- DOI
10.1142/S0129183124500293