A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives.

*(English)*Zbl 1268.65107Summary: 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, the dynamics of a giving up smoking model containing fractional derivatives is studied numerically. The multistep generalized differential transform method (for short MSGDTM) is employed to compute accurate approximate solutions to a giving up smoking model of fractional order. The unique positive solution for the fractional order model is presented. 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.

##### MSC:

65L99 | Numerical methods for ordinary differential equations |

34A08 | Fractional ordinary differential equations and fractional differential inclusions |

92C60 | Medical epidemiology |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |

##### Keywords:

fractional differential equations; mathematical model; smoking dynamics; differential transform method
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\textit{V. S. Ertürk} et al., Comput. Math. Appl. 64, No. 10, 3065--3074 (2012; Zbl 1268.65107)

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##### References:

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