论文信息 - The Homotopy Analysis Method for Approximating of Giving Up Smoking Model in Fractional Order

The Homotopy Analysis Method for Approximating of Giving Up Smoking Model in Fractional Order

In this paper, we consider the giving up smoking model. First, we present the giving up smoking model in fractional order. Then the homotopy analysis method (HAM) is employed to compute an approximate and analytical solution of the model in fractional order. The obtained results are compaired with those obtained by forth order Runge-Kutta method and nonstandard numerical method in the integer case. Finally, we present some numerical results.

Gul Zaman | Anwar Zeb | M. Ikhlaq Chohan

[1] Shaher Momani,et al. Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations , 2007, Comput. Math. Appl..

[2] Shaher Momani,et al. Homotopy perturbation method for nonlinear partial differential equations of fractional order , 2007 .

[3] S. Liao. Notes on the homotopy analysis method: Some definitions and theorems , 2009 .

[4] S. Momani,et al. The homotopy analysis method for handling systems of fractional differential equations , 2010 .

[5] I. Podlubny. Fractional differential equations , 1998 .

[6] Shaher Momani,et al. A reliable algorithm of homotopy analysis method for solving nonlinear fractional differential equations , 2010 .

[7] K. Miller,et al. An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[8] Gul Zaman,et al. Qualitative Behavior of Giving Up Smoking Models , 2011 .

[9] Ahmed Alawneh,et al. Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy analysis method , 2010, Comput. Math. Appl..

[10] Shaher Momani,et al. A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives , 2012, Comput. Math. Appl..

[11] R. Feynman,et al. RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING , 2003 .