Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order

Abstract

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.

Stability and Convergence Analysis of Smoking Impact in Society with Algorithm Aspects

“…Then [24] modified the proposed model and introduced a new class named as chain smokers. Later on, Zeb et al [25] studied a smoking model in which they argued local and global stability of the model and its general solutions in which the collaboration between occasional and potential smokers occurs. In [26] the author presented a modified smoking model in which the dynamic behavior has been discussed numerically.…”

“…The discrete method given in (22,25,29,32) is indeed an NSFD scheme because it is constructed according to Mickens rules [32] formalized as follows in [33]. Note that the denominator function φ is expected to better capture the dynamics of the continuous model through the presence of the underlying parameters d 3 , µ, γ.…”

“…Analysis of the scheme Proof: First, we prove the positivity of the scheme (22,25,29,32). It is easy to show that the NSFD scheme (22,25,29,32) takes the explicit form…”

“…Thus P k+1 ≥ 0, L k+1 ≥ 0, S k+1 ≥ 0, Q k+1 ≥ 0 whenever the discrete variables are non-negative at the previous iteration. It remains to prove the positive invariance of K. Adding the (22,25) and (29) we have…”

Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel

“…Considering the CaputoFabrizio-Caputo fractional derivative, the authors in [31] presented a new fractional giving up smoking model, the existence and uniqueness of the solution were discussed by the fixed point postulate. Zeb in [37] proposed a fractional smoking dynamic model considering adolescent nicotine dependence. In [10], the authors studied the giving up smoking dynamics using a fractional order model; approximate solutions via Laplace Adomian decomposition method were obtained.…”