Modelling and analysis of bad impact of smoking in society with Constant Proportional-Caputo Fabrizio operator

Smoking is now regarded as an epidemic because of the excessive mortality rate and large costs related to it. In line with the arena of the health enterprize, smoking is the third most common cause of mortality among human beings and the most preventable cause of sickness. Intending to study this problem, this manuscript frequently stresses the usage of the hybrid fractional differential operator to evaluate the dynamics of the fractional order quitting smoking version. We study a fractional-order version with a Constant Proportional-Caputo Fabrizio (CPCF) operator to investigate and examine the dynamical transmission of smoking. The qualitative analysis, and well-posedness of the fractional order system are examined. The analysis of the Volterra-type Lyapunov function for global stability is verified with the first and derivative tests. Also, Banach contraction characteristics are used to fulfil the criteria for the uniqueness of the exact solution. A complete discussion of additional analysis of the CPCF operator is furnished. In order to demonstrate the impacts of modifying the fractional order and to validate the theoretical findings, numerical simulations are carried out using an iterative Laplace transform method for a variety of fractional orders. The stability of the iterative scheme is also verified by using Picard's stable condition from the fixed point theorem. The CPCF operator has a broader definition than the Caputo–Fabrizio (CF) operator, and it elaborates on new insights into the mechanisms of smoking transmission throughout society.