• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.753-765
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• 2020

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, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding 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 also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.