ANALYSIS OF A FRACTIONAL ORDER SMOKING MODEL WITH RELAPSE AND HARMONIC MEAN TYPE INCIDENCE RATE UNDER 𠒜ℬ𠒞 OPERATOR

Lei Zhang, Tareq Saeed, Miao-Kun Wang, Nudrat Aamir and Muhammad Ibrahim
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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

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-13

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.

Keywords: Fractional Order Smoking Models; Existence and Uniqueness Results; Adam–Bashforth Method; Numerical Simulations (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401405

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