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A numeric-analytic method for approximating a giving up smoking model containing fractional derivatives. (English) Zbl 1268.65107
Summary: 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.
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