Warianty tytułu
Języki publikacji
Abstrakty
Smoking is the most lethal social poisoning event. The World Health Organization defines smoking as the most important preventable cause of disease. Around 4.9 million people worldwide die from smoking every year. In order to analysis this matter, we aim to investigate an e-cigarette smoking model with Atangana-Baleanu fractional derivative. We obtain the existence conditions of the solution for this fractional model utilizing fixed-point theory. After giving existence conditions, the uniqueness of the solution is proved. Finally, to show the effect of the Atangana-Baleanu fractional derivative on the model, we give some numerical results supported by illustrative graphics.
Rocznik
Tom
Strony
97--109
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- Department of Mathematics, Balıkesir University, Turkey., sucarr@gmail.com
autor
- Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, Turkey
autor
- Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, Turkey
autor
- Department of Mathematics, Faculty of Arts and Sciences, Balıkesir University, Turkey
Bibliografia
- [1] Atangana A., Baleanu D., New fractional derivatives with non-local and non-singular kernel Theory and Applications to Heat Transfer Model, Thermal Science, 20, 2016, 763-769.
- [2] Atangana, A., Koca, I., Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order, Chaos, Solitons & Fractals, 89, 2016, 447-454.
- [3] Evirgen F., Uçar S., Özdemir N., System analysis of HIV infection model with CD4+T under non-singular kernel derivative, Applied Mathematics and Nonlinear Sciences, 5, 1, 2020, 139-146.
- [4] Filatova D.V., Grzywaczewski M., Mathematical modeling in selected biological systems with fractional Brownian motion, 2008 Conference on Human System Interactions, IEEE, 2008, pp. 909-914.
- [5] Gülşen A., Uslu B., Health hazards and complications associated with electronic cigarettes: a review, Turkish Thoracic Journal, 2020, DOI: 10.5152/TurkThoracJ.2019.180203.
- [6] Gülşen A., Suicides with electronic cigarettes, General Internal Medicine, 2020, 81-88.
- [7] Hung J.H., Park A., Jung I.H., Qualitative and Sensitivity Analysis of the Effect of Electronic Cigarettes on Smoking Cessation, Computational and Mathematical Methods in Medicine, 2018, 2018.
- [8] Jajarmi A., Baleanu D., A new fractional analysis on the interaction of HIV with CD4+ T-cells, Chaos, Solitons & Fractals, 113, 2018, 221-229.
- [9] Jumarie G., New stochastic fractional models for Malthusian growth, the Poissonian birth process and optimal management of populations, Mathematical and Computer Modelling, 44(3-4), 2006, 231-254.
- [10] Khalid M., Khan F.S., Iqbal A., Perturbation-iteration algorithm to solve fractional giving up smoking mathematical model. International Journal of Computer Applications, 142, 9, 2016.
- [11] Kim J.S., Kim K., Electronic cigarette use and suicidal behaviors among adolescents, Journal of Public Health, 2019, DOI: 10.1093/pubmed/fdz086.
- [12] Koca I., Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators, The European Physical Journal Plus, 133:100, 2018.
- [13] Koca I., Analysis of rubella disease model with non-local and non-singular fractional derivatives, An International Journal of Optimization and Control: Theories & Applications, 8, 2018, 17-25.
- [14] Kumar S., Kumar R., Singh J., Nisar K.S., Kumar D., An efficient numerical scheme for fractional model of HIV-1 infection of CD4+ T-cells with the effect of antiviral drug therapy, Alexandria Engineering Journal, 2020, DOI: 10.1016/j.aej.2019.12.046.
- [15] Perelson A.S., Kirschner D.E., De Boer, R., Dynamics of HIV infection of CD4+ T cells, Mathematical Biosciences, 114, 1, 1993, 81-125.
- [16] Shabestari P.S., Panahi S., Hatef B., Jafari S., Sprott J.C., A new chaotic model for glucose-insulin regulatory system, Chaos, Solitons & Fractals, 112, 2018, 44-51.
- [17] Singh J., Kumar D., Hammouch Z., Atangana A., A fractional epidemiological model for computer viruses pertaining to a new fractional derivative, Applied Mathematics and Computation, 316, 2018, 504-515.
- [18] Straughan B., E-cigarette smoking with peer pressure, Mathematical Methods in the Applied Sciences, 42, 6, 2019, 2098–2108.
- [19] Toufik M., Atangana A., New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models, The European Physical Journal Plus, 2017, 132:444.
- [20] Uçar S., Uçar E., Özdemir N., Hammouch Z., Mathematical analysis and numerical simulation for a smoking model with Atangana-Baleanu derivative, Chaos, Solitons & Fractals, 118, 2019, 300-306.
- [21] Uçar S.,Özdemir N., Koca İ., Altun, E., Novel analysis of the fractional glucose–insulin regulatory system with non-singular kernel derivative, The European Physical Journal Plus, 135(6), 2020, 414.
- [22] WHO report on the global tobacco epidemic 2019, https://apps.who.int/iris/bitstream/handle/10665/326043/9789241516204-eng.pdf?ua=1, Accessed date: May 15, 2020.
- [23] Tobacco Free initiative - MPOWER measures, http://www.emro.who.int/tfi/mpower/index.html, Accessed date: May 15, 2020.
- [24] Yadav A., Srivastava P.K., Kumar A., Mathematical model for smoking: Effect of determination and education, International Journal of Biomathematics, 8, 1, 2015, 1550001.
- [25] Yavuz M., Özdemir, N., Analysis of an epidemic spreading model with exponential decay law, Mathematical Sciences and Applications E-Notes, 8, 1, 2020, 142-154.
- [26] Yavuz M., Yokus A., Analytical and numerical approaches to nerve impulse model of fractional-order, Numerical Methods for Partial Differential Equations, 2020, doi.org/10.1002/num.22476.
- [27] Yerlikaya-Özkurt F., Vardar-Acar C., Yolcu-Okur Y., Weber G.W., Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method, Journal of Computational and Applied Mathematics, 259, 2014, 843-850.
- [28] Zaman G., Optimal campaign in the smoking dynamics, Computational and Mathematical Methods in Medicine, 148, 2011, 9 pages.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-39afa023-06b2-410a-a6d4-dacdb54534a6