M. Zuriqat and A. A. Freihat, The multi-step Adomian decomposition method for approximating a fractional smoking habit model, Kyungpook Mathematical Journal., (2019) accepted

Smoking is one of the main causes of health problems and continues to be one of the world’s most signi…cant health challenges. In this paper, we obtain approximate analytical solutions of a mathematical fractional model of the evolution of smoking habit in the community using the multi-step Adomian decomposition method (MSADM). The proposed scheme is only a simple modi…cation of the Adomian decomposition method (ADM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for …nding accurate approximate solutions to the corresponding problems. A com- parative study between the new algorithm and the classical Runge-Kutta method is pre- sented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is e¤ective and convenient for solving linear and nonlinear differential equations of fractional order.