https://doi.org/10.1140/epjp/s13360-022-03413-z
Regular Article
A novel mathematical model of smoking: an integer and piece-wise fractional approach
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
Received:
20
August
2022
Accepted:
19
October
2022
Published online:
4
November
2022
The aim of this paper is to discuss different sorts of smokers in our society with the help of a new mathematical model to discuss the behaviour of smokers in our society. We formulate new model by taking the variable coefficients as functions of cosine. We use both integer and piece-wise operator to analyse the evolution of the proposed model. We attain equilibrium points and explore the local and global stability of the model. With help of Leverrier–Faddeev method and Routh–Hurwitz criterion, the result of local stability is demonstrated. The global stability is derived via Lasalls invariance method. The numerical solution for piecewise model is presented via Adams-Bashforth technique based on Newton polynomial. We simulate the numerical results for specific values of parameters to visualize the cross over behaviour.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
