IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v141y2020ics0960077920307049.html
   My bibliography  Save this article

Dynamical Characteristics and Signal Flow Graph of Nonlinear Fractional Smoking Mathematical Model

Author

Listed:
  • Mahdy, A.M.S.
  • Mohamed, M.S.
  • Gepreel, K.A.
  • AL-Amiri, A.
  • Higazy, M.

Abstract

In this article, we study approximate analytic solutions for one of the famous models in biomathematics, namely the nonlinear fractional mathematical smoking model. When alpha=1, we deduce the analytical solution using the Reduced differential transforms method (RDTM) for the nonlinear ordinary mathematical smoking model. The disease-free equilibrium point, the stability of the equilibrium point, and the reproduction number are all discussed for the fractional mathematical smoking model. We use mathematical software packages such as Mathematica to find more iteration when calculating the approximate solution. Results are presented graphically to illustrate the behavior of the obtained approximate solutions. The system is presented by a proposed novel signal flow graph and simulated via SIMULINK/MATLAB. The graph of signal flow is used to calculate some of the model invariants such as the adjacency matrix, model energy, and Estrada index. Also, the novelty and significance of the results are clear using a 3D plot.

Suggested Citation

  • Mahdy, A.M.S. & Mohamed, M.S. & Gepreel, K.A. & AL-Amiri, A. & Higazy, M., 2020. "Dynamical Characteristics and Signal Flow Graph of Nonlinear Fractional Smoking Mathematical Model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307049
    DOI: 10.1016/j.chaos.2020.110308
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920307049
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110308?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mridula Garg & Pratibha Manohar & Shyam L. Kalla, 2011. "Generalized Differential Transform Method to Space-Time Fractional Telegraph Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-9, October.
    2. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    3. Singh, Jagdev & Kumar, Devendra & Baleanu, Dumitru & Rathore, Sushila, 2018. "An efficient numerical algorithm for the fractional Drinfeld–Sokolov–Wilson equation," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 12-24.
    4. K. A. Gepreel & M. Higazy & A. M. S. Mahdy, 2020. "Optimal control, signal flow graph, and system electronic circuit realization for nonlinear Anopheles mosquito model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(09), pages 1-18, September.
    5. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    6. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chimmula, Vinay Kumar Reddy & Zhang, Lei, 2020. "Time series forecasting of COVID-19 transmission in Canada using LSTM networks," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2022. "Ergodic stationary distribution of stochastic epidemic model for HBV with double saturated incidence rates and vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Danane, Jaouad & Allali, Karam & Hammouch, Zakia, 2020. "Mathematical analysis of a fractional differential model of HBV infection with antibody immune response," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Saad, Khaled M. & Gómez-Aguilar, J.F. & Almadiy, Abdulrhman A., 2020. "A fractional numerical study on a chronic hepatitis C virus infection model with immune response," Chaos, Solitons & Fractals, Elsevier, vol. 139(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. Ain, Qura tul & Khan, Aziz & Ullah, Muhammad Irfan & Alqudah, Manar A. & Abdeljawad, Thabet, 2022. "On fractional impulsive system for methanol detoxification in human body," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    7. Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2020. "Stochastic permanence of an epidemic model with a saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. Tabassum, Muhammad Farhan & Saeed, Muhammad & Akgül, Ali & Farman, Muhammad & Chaudhry, Nazir Ahmad, 2020. "Treatment of HIV/AIDS epidemic model with vertical transmission by using evolutionary Padé-approximation," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    10. El-Sayed, A.M.A. & Rida, S.Z. & Gaber, Y.A., 2020. "Dynamical of curative and preventive treatments in a two-stage plant disease model of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    11. Jena, Rajarama Mohan & Chakraverty, Snehashish & Jena, Subrat Kumar, 2020. "Analysis of the dynamics of phytoplankton nutrient and whooping cough models with nonsingular kernel arising in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    12. Kritika, & Agarwal, Ritu & Purohit, Sunil Dutt, 2020. "Mathematical model for anomalous subdiffusion using comformable operator," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    13. Fawaz E. Alsaadi & Amirreza Yasami & Christos Volos & Stelios Bekiros & Hadi Jahanshahi, 2023. "A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    14. Prakash, Amit & Kaur, Hardish, 2021. "Analysis and numerical simulation of fractional Biswas–Milovic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 298-315.
    15. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    16. Ullah, Ihsan & Ahmad, Saeed & Rahman, Mati ur & Arfan, Muhammad, 2021. "Investigation of fractional order tuberculosis (TB) model via Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    17. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2018. "Novel numerical method for solving variable-order fractional differential equations with power, exponential and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 175-185.
    18. Fatima, Bibi & Zaman, Gul, 2020. "Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    19. Yavuz, Mehmet & Bonyah, Ebenezer, 2019. "New approaches to the fractional dynamics of schistosomiasis disease model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 373-393.
    20. Mahmoud, Emad E. & Trikha, Pushali & Jahanzaib, Lone Seth & Almaghrabi, Omar A., 2020. "Dynamical analysis and chaos control of the fractional chaotic ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307049. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.