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Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative

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  • Uçar, Sümeyra
  • Uçar, Esmehan
  • Özdemir, Necati
  • Hammouch, Zakia

Abstract

This paper ensures meticulous mathematical study for analyzing the dynamics of smoking model and its public health with Atangana–Baleanu derivative. The existence and uniqueness problems to relevant model are examined via fixed point theory. The results are implemented by giving some illustrative graphics including the variation of fractional order.

Suggested Citation

  • Uçar, Sümeyra & Uçar, Esmehan & Özdemir, Necati & Hammouch, Zakia, 2019. "Mathematical analysis and numerical simulation for a smoking model with Atangana–Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 300-306.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:300-306
    DOI: 10.1016/j.chaos.2018.12.003
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    1. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    2. Alkahtani, Badr Saad T. & Atangana, Abdon, 2016. "Analysis of non-homogeneous heat model with new trend of derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 566-571.
    3. Jagdev Singh & Devendra Kumar & Adem Kılıçman, 2014. "Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, August.
    4. Singh, Jagdev & Kumar, Devendra & Hammouch, Zakia & Atangana, Abdon, 2018. "A fractional epidemiological model for computer viruses pertaining to a new fractional derivative," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 504-515.
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    Cited by:

    1. Thabet Abdeljawad & Arran Fernandez, 2019. "On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels," Mathematics, MDPI, vol. 7(9), pages 1-13, August.
    2. Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Mallika Arjunan, M. & Hamiaz, A. & Kavitha, V., 2021. "Existence results for Atangana-Baleanu fractional neutral integro-differential systems with infinite delay through sectorial operators," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).
    4. Zafar, Zain Ul Abadin & Zaib, Sumera & Hussain, Muhammad Tanveer & Tunç, Cemil & Javeed, Shumaila, 2022. "Analysis and numerical simulation of tuberculosis model using different fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    5. Kucche, Kishor D. & Sutar, Sagar T., 2021. "Analysis of nonlinear fractional differential equations involving Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Nguiwa, Tchule & Kolaye, Gabriel Guilsou & Justin, Mibaile & Moussa, Djaouda & Betchewe, Gambo & Mohamadou, Alidou, 2021. "Dynamic study of SIAISQVR−B fractional-order cholera model with control strategies in Cameroon Far North Region," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Asif, Muhammad & Ali Khan, Zar & Haider, Nadeem & Al-Mdallal, Qasem, 2020. "Numerical simulation for solution of SEIR models by meshless and finite difference methods," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    8. Dumitru Baleanu & Arran Fernandez, 2019. "On Fractional Operators and Their Classifications," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    9. Mansal, Fulgence & Sene, Ndolane, 2020. "Analysis of fractional fishery model with reserve area in the context of time-fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    10. Gao, Wei & Ghanbari, Behzad & Baskonus, Haci Mehmet, 2019. "New numerical simulations for some real world problems with Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 34-43.
    11. Dutta, Maitreyee & Roy, Binoy Krishna, 2020. "A new fractional-order system displaying coexisting multiwing attractors; its synchronisation and circuit simulation," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    12. Hu Zhang & Anwar Zeb & Aying Wan & Zizhen Zhang, 2022. "Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    13. Dineshkumar, C. & Udhayakumar, R. & Vijayakumar, V. & Nisar, Kottakkaran Sooppy & Shukla, Anurag, 2022. "A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    14. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
    16. Akgül, Ali & Fatima, Umbreen & Iqbal, Muhammad Sajid & Ahmed, Nauman & Raza, Ali & Iqbal, Zafar & Rafiq, Muhammad, 2021. "A fractal fractional model for computer virus dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    17. Kumar, Ashish & Pandey, Dwijendra N., 2020. "Existence of mild solution of Atangana–Baleanu fractional differential equations with non-instantaneous impulses and with non-local conditions," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    18. Sutar, Sagar T. & Kucche, Kishor D., 2021. "On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    19. Sina Etemad & Albert Shikongo & Kolade M. Owolabi & Brahim Tellab & İbrahim Avcı & Shahram Rezapour & Ravi P. Agarwal, 2022. "A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability," Mathematics, MDPI, vol. 10(22), pages 1-31, November.
    20. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    21. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

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