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

Abstract

This paper investigates the newly constructed fractional order (FO) smoking model with relapse and harmonic mean type incidence rate under the fractional operator [Formula: see text]. 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.