Investigation of the Solution of a Smoking Model with Conformable Derivative

This paper is designed to generalize one of the important biomathematical models that studies and analyses smoking spread in a given population within the framework of conformable derivative. The use of conformable operator instead of the classical integer order generalizes the epidemic model and gives us the opportunity of obtaining variety of results and expectations. Due to the difficulty of solving non-linear fractional systems, we use two analytical-approximate techniques to solve this model. The first technique is the residual power series method, which depends on minimizing the residual error of the equation under study. The second method is the Laplace decomposition method, which forms an efficient combination between Laplace transform and the well-known Adomian decomposition method. Both methods effectively solve different types of problems, including ordinary and partial differential equations of classical integer or fractional orders, with high accuracy and without the need for linearization or discretization. In this paper, we apply both techniques to the conformable smoking model (CSM). Some numerical and graphical results for different values of the conformable derivative allow us to notice the effect of this conformable operator to the solution curves of the CSM. Moreover, some numerical results for the residual error are tabulated to assess the accuracy of our outcomes. The results show the simplicity, efficiency, rapid convergence and accuracy of both analytical methods. In fact, for the same number of iterations, both methods produce identical results.