Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order

Anwar Zeb; Gul Zaman; Vedat Suat Erturk; Baha Alzalg; Faisal Yousafzai; Madad Khan

doi:10.1371/journal.pone.0103617

Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order

PLoS One. 2016 Apr 22;11(4):e0103617. doi: 10.1371/journal.pone.0103617. eCollection 2016.

Authors

Anwar Zeb¹, Gul Zaman², Vedat Suat Erturk³, Baha Alzalg⁴, Faisal Yousafzai⁵, Madad Khan¹

Affiliations

¹ Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, KPK, Pakistan.
² Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan.
³ Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayis University, 55139, Samsun, Turkey.
⁴ Department of Mathematics, The University of Jordan, Amman 11942, Jordan.
⁵ Department of Mathematics, COMSATS Institute of Information Technology Attack, Pakistan.

Abstract

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.

MeSH terms

Adolescent
Adolescent Behavior*
Algorithms
Humans
Models, Theoretical*
Smoking Cessation* / psychology
Smoking Cessation* / statistics & numerical data
Statistics as Topic / methods
Tobacco Use Disorder / epidemiology
Tobacco Use Disorder / therapy*

Grants and funding

The authors received no specific funding for this work.