Fractional analog of a chemical system inspired by Braess' paradox

Mizrak O. O., ÖZALP N.

COMPUTATIONAL & APPLIED MATHEMATICS, cilt.37, sa.3, ss.2503-2518, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s40314-017-0462-9
  • Dergi Adı: COMPUTATIONAL & APPLIED MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2503-2518
  • Anahtar Kelimeler: Kinetic models, Chemical networks, Braess' paradox, Fractional derivative, Existence and uniqueness, Stability, DIFFERENTIAL-EQUATIONS, PREDATOR-PREY, MODEL, RECOGNITION, STABILITY
  • Ankara Üniversitesi Adresli: Evet

Özet

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.