AIMS Mathematics, 2020, 5(2): 781-797. doi: 10.3934/math.2020053

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A fractional order alcoholism model via Caputo-Fabrizio derivative

Department of Mathematics, Ağrı İbrahim Çeçen University, Ağrı, Turkey

A fractional order mathematical model of the Caputo-Fabrizio type is presented for an alcoholism model. The existence and the uniqueness of the alcoholism model were investigated by using a fixed-point theorem. Numerical solutions for the model were obtained by using special parameter values.
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1. M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 1-13.

2. J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87-92.

3. M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geophys. J. Int., 13 (1967), 529-539.    

4. I. Podlubny, Fractional Differential Equations, San Diego: Academic Press, 1999.

5. H. F. Huo, X. M. Zhang, Complex dynamics in an alcoholism model with the impact of Twitter, Math. Biosci., 281 (2016), 24-35.    

6. A. Behnood, F. L. Mannering, The effects of drug and alcohol consumption on driver injury severities in single-vehicle crashes, Traffic Inj. Prev., 18 (2017), 456-462.    

7. J. F. Gómez-Aguilar, A. Atangana, New insight in fractional differentiation: Power, exponential decay and Mittag-Leffler laws and applications, Eur. Phys. J. Plus, 132 (2017), 13.

8. J. F. Gómez-Aguilar, A. Atangana, A new derivative with normal distribution kernel: Theory, methods and applications, Physica A, 476 (2017), 1-14.    

9. J. F. Gómez-Aguilar, A. Atangana, Fractional derivatives with no-index law property: application to chaos and statistics, Chaos, Soliton. Fract., 114 (2018), 516-535.    

10. J. F. Gómez-Aguilar, A. Atangana, V. F. Morales-Delgado, Electrical circuits RC, LC, and RL described by Atangana-Baleanu fractional derivatives, Int. J. Circ. Theor. App., 45 (2017), 1514-1533.    

11. J. F. Gómez-Aguilar, V. Morales-Delgado, M. Taneco-Hernández, et al. Analytical solutions of the electrical RLC circuit via Liouville-Caputo operators with local and non-local kernels, Entropy, 18 (2016), 402.

12. J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, M. G. López-López, et al. Atangana-Baleanu fractional derivative applied to electromagnetic waves in dielectric media, J. Electromagnet. Wave., 30 (2016), 1937-1952.    

13. H. Yépez-Martínez, J. F. Gómez-Aguilar, A new modified definition of Caputo-Fabrizio fractional-order derivative and their applications to the Multi Step Homotopy Analysis Method (MHAM), J. Comput. Appl. Math., 346 (2019), 247-260.    

14. J. F. Gómez-Aguilar, Behavior characteristics of a cap-resistor, memcapacitor, and a memristor from the response obtained of RC and RL electrical circuits described by fractional differential equations, Turk. J. Electr. Eng. Comput. Sci., 24 (2016), 1421-1433.    

15. N. A. Sheikh, F. Ali,, M. Saqib, et al. Comparison and analysis of the Atangana-Baleanu and Caputo-Fabrizio fractional derivatives for generalized Casson fluid model with heat generation and chemical reaction, Results phys., 7 (2017), 789-800.    

16. J. Connor, Alcohol consumption as a cause of cancer, Addiction, 112 (2017), 222-228.    

17. K. Ma, Z. Baloch, T. T. He, et al. Alcohol consumption and gastric cancer risk: A meta-analysis, Med. Sci. Monit., 23 (2017), 238-246.    

18. S. Lee, E. Jung, C. Castillo-Chavez, Optimal control intervention strategies in low- and high-risk problem drinking populations, Socio-Econ. Plan. Sci., 44 (2010), 258-265.    

19. H. F. Huo, Y. L. Chen, H. Xiang, Stability of a binge drinking model with delay, J. Biol. Dynam., 11 (2017), 210-225.    

20. H. F. Huo, S. H. Ma, X. Y. Meng, Modelling alcoholism as a contagious disease: A mathematical model with awareness programs and time delay, Discrete Dyn. Nat. Soc., 2015 (2015), 260195.

21. J. L. Manthey, A. Y. Aidoob, Campus drinking: An epidemiolodical model, J. Biol. Dynam., 2 (2008), 346-356.    

22. H. F. Huo, X. M. Zhang, Complex dynamics in an alcoholism model with the impact of Twitter, Math. Biosci., 281 (2016), 24-35.    

23. H. Woo, C. H. Sung, E. Shim, et al. Identification of keywords from Twitter and web blog posts to detect influenza epidemics in Korea, Disaster Med. Public, 12 (2018), 352-359.    

24. H. F. Huo, X. M. Zhang, Modeling the influence of twitter in reducing and increasing the spread of influenza epidemics, SpringerPlus, 5 (2016), 88.

25. J. Gomide, A. Veloso, W. Meira, et al. Dengue surveillance based on a computational model of spatiotemporal locality of Twitter, Proceedings of the 3rd International Web Science Conference, 1 (2017), 1-3.

26. S. Diane, D. Njankou, F. Nyabadza, Modelling the potential role of media campaigns in Ebola transmission dynamics, Int. J. Differ. Equ., 2017 (2017), 3758269.

27. J. F. Gómez-Aguilar, Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations, Physica A, 494 (2018), 52-75.    

28. J. K. Zhou, Differential Transformation and Its Applications for Electrical Circuits (in Chinese), China: Huazhong University Press, 1986, 1279-1289.

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