Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 2: 781-797. doi: 10.3934/math.2020053
Previous Article Next Article
Research article

A fractional order alcoholism model via Caputo-Fabrizio derivative

  • Department of Mathematics, Ağrı İbrahim Çeçen University, Ağrı, Turkey
  • Received: 08 October 2019 Accepted: 19 December 2019 Published: 25 December 2019

  • MSC : 26A33, 34K28, 39A14, 93A30

  • 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.

    Citation: Mustafa Ali Dokuyucu. A fractional order alcoholism model via Caputo-Fabrizio derivative[J]. AIMS Mathematics, 2020, 5(2): 781-797. doi: 10.3934/math.2020053

    Related Papers:

  • 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.


    加载中


    [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.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(4253) PDF downloads(771) Cited by(33)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(1)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog