Mohammad Zurigat, The multi-step analytic method and application for approximating a giving up fractional smoking model, Analele Universitatii Oradea Fasc. Matematica, Tom XX, (1) (2013), 177-188.

Smoking is one of the main health problems and health challenges in the word. This paper presents approximate analytical solutions to a giving up smoking model of fractional order using the multi-step homotopy analysis method (MHAM). The proposed scheme is only a simple modication of the homotopy analysis method, 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 comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are presented graphically.