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

Vedat Suat Erturk; Gul Zaman; Baha Alzalg; Anwar Zeb; Shaher Momani

doi:10.1007/s40995-017-0278-x

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

Vedat Suat Erturk
, Gul Zaman
, Baha Alzalg
, Anwar Zeb
, Shaher Momani

Ondokuz Mayis University
University of Malakand
University of Jordan
COMSATS University Islamabad

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	569-575
Number of pages	7
Journal	Iranian Journal of Science and Technology, Transaction A: Science
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s40995-017-0278-x
State	Published - 1 Sep 2017
Externally published	Yes

Keywords

Caputo fractional derivative
Differential transform method
Generalized Euler method
Numerical solution
Smoking dynamics

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10.1007/s40995-017-0278-x

Cite this

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

abstract = "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.",

keywords = "Caputo fractional derivative, Differential transform method, Generalized Euler method, Numerical solution, Smoking dynamics",

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doi = "10.1007/s40995-017-0278-x",

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T1 - Comparing Two Numerical Methods for Approximating a New Giving Up Smoking Model Involving Fractional Order Derivatives

AU - Erturk, Vedat Suat

AU - Zaman, Gul

AU - Alzalg, Baha

AU - Zeb, Anwar

AU - Momani, Shaher

PY - 2017/9/1

Y1 - 2017/9/1

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AB - 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.

KW - Caputo fractional derivative

KW - Differential transform method

KW - Generalized Euler method

KW - Numerical solution

KW - Smoking dynamics

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DO - 10.1007/s40995-017-0278-x

M3 - Article

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EP - 575

JO - Iranian Journal of Science and Technology, Transaction A: Science

JF - Iranian Journal of Science and Technology, Transaction A: Science

IS - 3

ER -

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

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Keywords

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