A new fractional analysis on the polluted lakes system

BİLDİK N., DENİZ S.

Chaos, Solitons and Fractals, vol.122, pp.17-24, 2019 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Review
  • Volume: 122
  • Publication Date: 2019
  • Doi Number: 10.1016/j.chaos.2019.02.001
  • Journal Name: Chaos, Solitons and Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.17-24
  • Keywords: Atangana–Baleanu derivative, Systems of fractional differential equations, Water pollution
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this paper, we use Atangana–Baleanu derivative which is defined with the Mittag–Leffler function and has all the properties of a classical fractional derivative for solving the system of fractional differential equations. The classical model of polluted lakes system is modified by using the concept of fractional differentiation with nonsingular and nonlocal fading memory. The new numerical scheme recommended by Toufik and Atangana is used to analyze the modified model of polluted lakes system. Some numerical illustrations are presented to show the effect of the new fractional differentiation.