IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i05ns0218348x22401405.html
   My bibliography  Save this article

Analysis Of A Fractional Order Smoking Model With Relapse And Harmonic Mean Type Incidence Rate Under Ð ’Œâ„¬Ð ’Ž Operator

Author

Listed:
  • LEI ZHANG

    (School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, P. R. China)

  • TAREQ SAEED

    (��Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

  • MIAO-KUN WANG

    (��Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China§Institute for Advanced Study Honoring Chen Jian Gong, Hangzhou Normal University, Hangzhou 311121, P. R. China)

  • NUDRAT AAMIR

    (�Department of Basic Sciences and Humanities, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan)

  • MUHAMMAD IBRAHIM

    (��Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia¶Department of Basic Sciences and Humanities, CECOS University of IT and Emerging Sciences, Peshawar, Pakistan)

Abstract

This paper investigates the newly constructed fractional order (FO) smoking model with relapse and harmonic mean type incidence rate under the fractional operator 𠒜ℬ𠒞. Furthermore, for the model considered, the existence results and uniqueness of the solution are established with the help of the fixed point theory approach. The stability of the model is proven with the help of Ulam–Hyres approach by considering small perturbation in the problem. The iterative FO Adams–Bashforth technique is considered for obtaining the numerical solution. Moreover, the established scheme is simulated against the available data for some smoking communities where various types of potential, moderate and quit smokers are living. However, different fractional orders are used for simulation and it is evident through the results that FO converges to integer order as order is increased. Moreover, smoking may also be controlled through education, employment and the awareness of its harmfulness by doctors and their dosage of some drugs.

Suggested Citation

  • Lei Zhang & Tareq Saeed & Miao-Kun Wang & Nudrat Aamir & Muhammad Ibrahim, 2022. "Analysis Of A Fractional Order Smoking Model With Relapse And Harmonic Mean Type Incidence Rate Under Ð ’Œâ„¬Ð ’Ž Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-13, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401405
    DOI: 10.1142/S0218348X22401405
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22401405
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X22401405?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.

    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:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401405. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.