Fractal Calculus of Variations: A New Framework

Golmankhaneh A. K., Tunç C., Depollier C., Zayed A. I.

Analysis and Mathematical Physics, cilt.15, sa.5, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 5
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s13324-025-01128-9
  • Dergi Adı: Analysis and Mathematical Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: 28A80, 34A34, 83C57, Calculus of variations, Fractal calculus, Fractal Euler equation, Optical fractal path, Shortest distance in fractal space
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we give a short summary of fractal calculus. We introduce the concept of fractal variation of calculus and derive the general form of the fractal Euler equation, along with an alternate form. We explore applications of the fractal Euler equation, including the optical fractal path near the event horizon of a black hole and determining the shortest distance in fractal space. Examples and illustrative plots are provided to demonstrate the detailed behavior of these equations and their practical implications.