Comparing two numerical methods for approximating a new giving up smoking model with fractional order derivative

Document Type : Regular Paper


1 Ondokuz Mayis University

2 Department of Mathematics, Abdul Wali Khan University Mardan KPK Pakistan

3 University of Jordan · Department of Mathematics

4 Department of Mathematics COMSATS Institute of Information Technology, Abbottabad, KPK Pakistan

5 The University of Jordan


In a recent paper [1], the authors presented a new model of giving up smoking model. In the present paper, the dynamics of this new model involving the Caputo derivative was studied numerically. For this purpose, generalized Euler method and the multistep generalized differential transform method are employed to compute accurate approximate solutions to this new giving up smoking model of fractional order. The unique positive solution for the fractional order model is presented. A comparative study between these two methods and the well known Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically.


Main Subjects