A numeric–analytic method for approximating a giving up smoking model containing fractional derivatives

Smoking is one of the main causes of health problems and continues to be one of the world’s most significant health challenges. In this paper, the dynamics of a giving up smoking model containing fractional derivatives is studied numerically. The multistep generalized differential transform method (for short MSGDTM) is employed to compute accurate approximate solutions to a giving up smoking model of fractional order. The unique positive solution for the fractional order model is presented. 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 also presented graphically.