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## 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  May 2019 Published  December 2019

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. In this work, we principally aim to thoroughly examine a smoking model as affected by determination and education-related activities through Caputo-Fabrizio and Atangana-Baleanu derivatives. We use fixed point method making it possible for us to trace the proof of existence and uniqueness results for both fractional order models. We theoretically display the effectual features of the aforementioned fractional models, verifying the results via numerical graphics with different 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 & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020178
##### References:

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##### References:
Numerical simulations for the model (7) at $\sigma = 0.93$ and $\sigma = 0.75$, respectively
Numerical simulations for the model (8) at $\sigma = 0.93$ and $\sigma = 0.75$, 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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