Kyungpook Mathematical Journal 2020; 60(4): 753-765
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
The Multi-step Adomian Decomposition Method for Approximating a Fractional Smoking Habit Model
Mohammad Zuriqat*, Asad Freihat
Department of Mathematics, Al al-Bayt University, P. O. Box 130095 Mafraq, Jordan
e-mail : firstname.lastname@example.org
Department of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, Jordan
e-mail : email@example.com
Received: June 10, 2015; Accepted: June 21, 2019
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.
Keywords: fractional differential equations, multi-step Adomian decomposition method, smoking model, numerical analysis, mathematical fractional model