An approach for approximate solution of fractional-order smoking model with relapse class


Zeb A., Ertürk V. S., Khan U., Zaman G., Momani S.

INTERNATIONAL JOURNAL OF BIOMATHEMATICS, vol.11, no.6, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 6
  • Publication Date: 2018
  • Doi Number: 10.1142/s1793524518500778
  • Journal Name: INTERNATIONAL JOURNAL OF BIOMATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Mathematical model, reproductive number, next generation matrix method, stability analysis, Grunwald-Letnikov method, numerical simulation, NANOFLUID HEAT-TRANSFER, MAGNETIC-FIELD, DIFFERENTIAL-EQUATIONS, NUMERICAL-SIMULATION, NATURAL-CONVECTION, POROUS ENCLOSURE, LORENTZ FORCES, ELECTRIC-FIELD, FLOW, CAVITY
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, we develop a fractional-order smoking model by considering relapse class. First, we formulate the model and find the unique positive solution for the proposed model. Then we apply the Grunwald-Letnikov approximation in the place of maintaining a general quadrature formula approach to the Riemann-Liouville integral definition of the fractional derivative. Building on this foundation avoids the need for domain transformations, contour integration or involved theory to compute accurate approximate solutions of fractional-order giving up smoking model. A comparative study between Grunwald-Letnikov method and Runge-Kutta method is presented in the case of integer-order derivative. Finally, we present the obtained results graphically.