Fractional analog of a chemical system inspired by Braess' paradox
COMPUTATIONAL & APPLIED MATHEMATICS, vol.37, no.3, pp.2503-2518, 2018 (SCI-Expanded, Scopus)
- 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.