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

Ertürk V. S., Zaman G., Momani S.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.64, no.10, pp.3065-3074, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 10
  • Publication Date: 2012
  • Doi Number: 10.1016/j.camwa.2012.02.002
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3065-3074
  • Keywords: Fractional differential equations, Mathematical model, Smoking dynamics, Differential transform method, DIFFERENTIAL TRANSFORM METHOD, EQUATIONS
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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. (C) 2012 Elsevier Ltd. All rights reserved.