Analyzing the stability of fractal delay differential equations

Khalili Golmankhaneh A., Tunç C.

Chaos, Solitons and Fractals, cilt.188, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 188
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.chaos.2024.115492
  • Dergi Adı: Chaos, Solitons and Fractals
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: Fractal calculus, Fractal delay differential, Predictor–corrector scheme, Stability of the fractal Mackey–Glass
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we provide a comprehensive overview of fractal calculus and investigate the stability of both linear and non-linear fractal delay differential equations with fractal support. Our analysis encompasses the stability of the fractal Mackey–Glass equation as well as fractal differential equations with single and dual delays. Additionally, we introduce a predictor–corrector scheme to solve the fractal one-delay differential equation. Several examples are presented to illustrate the effects of fractal-order differentiation, which arise from the dimensionality of the fractal support, and the impact of fractal delays.