Fractional model of smoking with relapse and harmonic mean type incidence rate under Caputo operator

In this manuscript, we have analyzed a new time non-integer order smoking model endowed with Caputo fractional type derivative operator. The is composed of four compartmental agents various smokers named as potential smoker, Light Smoker and Quit smoker. first attempt about the qualitative study considered problem along existing result derivation unique solution by application fixed point theory. Secondly, for semi-analytical model, very famous technique Generalized Adams–Bashforth Moulton method used. Numerical simulation different integer laying between (0, 1) has been drawn using Matlab. For initial data, depicts stable shows convergence single point. Smaller orders show good results in framework stability.