Comparing Two Numerical Methods for Approximating a New Giving Up Smoking Model Involving Fractional Order Derivatives

Ertürk V. S., Zaman G., Alzalg B., Zeb A., Momani S.

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, cilt.41, sa.A3, ss.569-575, 2017 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: A3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1007/s40995-017-0278-x
  • Dergi Adı: IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.569-575
  • Anahtar Kelimeler: Generalized Euler method, Differential transform method, Caputo fractional derivative, Smoking dynamics, Numerical solution, PARTIAL-DIFFERENTIAL-EQUATIONS, TRANSFORM METHOD
  • Ondokuz Mayıs Üniversitesi Adresli: Evet

Özet

In a recent paper (Zeb et al. in Appl Math Model 37(7):5326-5334, 2013), the authors presented a new model of giving up smoking model. In the present paper, the dynamics of this new model involving the Caputo derivative was studied numerically. For this purpose, generalized Euler method and the multistep generalized differential transform method are employed to compute accurate approximate solutions to this new giving up smoking model of fractional order. The unique positive solution for the fractional order model is presented. A comparative study between these two methods and the well-known Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically.