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Z. Odibat, S. Momani and H. Xu, “A Reliable Algorithm of Homotopy Analysis Method for Solving Nonlinear Fractional Differential Equations,” Applied Mathematical Modelling, Vol. 34, No. 3, 2010, pp. 593-600. doi:10.1016/j.apm.2009.06.025

has been cited by the following article:

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

  AUTHORS: Anwar Zeb, M. Ikhlaq Chohan, Gul Zaman

  KEYWORDS: Fractional Differential Equations; Epidemic Model; Homotopy Analysis Method

  JOURNAL NAME: Applied Mathematics, Vol.3 No.8, August 1, 2012

  ABSTRACT: 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.