# American Institute of Mathematical Sciences

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July  2021, 14(7): 2571-2589. doi: 10.3934/dcdss.2020178

## Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives

 Department of Mathematics, Balıkesir University, Balıkesir 10145, Turkey

* Corresponding author: Sümeyra Uçar

Received  April 2019 Revised  January 2021 Published  July 2021 Early access  May 2021

These days, it is widely known that smoking causes numerous diseases, as well as resulting in many avoidable losses of life globally, and therefore encumbers the society with enormous unnecessary burdens. The aim of this study is to examine in-depth a smoking model that is mainly influenced by determination and educational actions via CF and AB derivatives. For both fractional order models, the fixed point method is used, which allows us to follow the proof of existence and the results of uniqueness. The effective properties of the above-mentioned fractional models are theoretically exhibited, their results are confirmed by numerical graphs by various fractional orders.

Citation: Sümeyra Uçar. Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2571-2589. doi: 10.3934/dcdss.2020178
##### References:

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##### References:
Numerical simulations for the model (7) at $\sigma = 0.93$, $\sigma = 0.75$ and $\sigma = 0.6$, respectively
Numerical simulations for the model (8) at $\sigma = 0.93$, $\sigma = 0.75$ and $\sigma = 0.6$ respectively
The effect of the parameters $a_{4}$ on the smokers population $s$ of the model (7) for the fractional order $\sigma = 0.95$ and $\sigma = 0.75$, respectively
The effect of the parameters $a_{4}$ on the smokers population $s$ of the model (8) for the fractional order $\sigma = 0.95$ and $\sigma = 0.75$, respectively
The effect of the parameters $a_{5}$ on the smokers population $s$ of the model (7) for the fractional order $\sigma = 0.95$ and $\sigma = 0.75$, respectively
The effect of the parameters $a_{5}$ on the smokers population $s$ of the model (8) for the fractional order $\sigma = 0.95$ and $\sigma = 0.75$, respectively
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