Fractal calculus of variations for problems with constraints

Golmankhaneh A. K., Cattani C., Pasechnik R., Furuichi S., Jorgensen P. E. T.

Modern Physics Letters A, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1142/s0217732325500014
  • Dergi Adı: Modern Physics Letters A
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: constraints, Fractal calculus, fractal variational calculus, Lagrangian multipliers
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we present a summary of fractal calculus and propose the use of Lagrange multipliers for both fractal calculus and fractal variational calculus with constraints. We examine the application of these methods across various branches of physics. By employing fractal variational calculus with constraints, we derive fundamental equations such as the fractal mechanical wave equation, the fractal Schrödinger equation in quantum mechanics, Maxwell's equations in fractal electromagnetism, and the Lagrange equation for constraints in fractal classical mechanics. Several examples are provided to illustrate these concepts in detail.