Fractional analog of a chemical system inspired by Braess' paradox

Mizrak O. O., ÖZALP N.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.37, no.3, pp.2503-2518, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1007/s40314-017-0462-9
  • Journal Name: COMPUTATIONAL & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2503-2518
  • Keywords: Kinetic models, Chemical networks, Braess' paradox, Fractional derivative, Existence and uniqueness, Stability, DIFFERENTIAL-EQUATIONS, PREDATOR-PREY, MODEL, RECOGNITION, STABILITY
  • Ankara University Affiliated: Yes

Abstract

In this paper, we introduce the fractional analog of a chemical model arouse from a mathematical paradox attributed to Dietrich Braess. Two basic examples which serve fractional kinetic models as better suited models to the real data sets than the integer-order counterparts are given. Existence and uniqueness of the rebuilt model's solutions are proved. It is shown that asymptotic stability conditions of the solutions are provided. A comparison is made between two different solution methods and numerical simulations are also presented to exemplify the mathematical outcomes.