Classical mechanics on fractal curves

Golmankhaneh A., Welch K., Tunç C., Gasimov Y. S.

European Physical Journal: Special Topics, cilt.232, sa.7, ss.991-999, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 232 Sayı: 7
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1140/epjs/s11734-023-00775-y
  • Dergi Adı: European Physical Journal: Special Topics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC
  • Sayfa Sayıları: ss.991-999
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Fractal analogue of Newton, Lagrange, Hamilton, and Appell’s mechanics are suggested. The fractal α-velocity and α-acceleration are defined in order to obtain the Langevin equation on fractal curves. Using the Legendre transformation, Hamilton’s mechanics on fractal curves is derived for modeling a non-conservative system on fractal curves with fractional dimensions. Fractal differential equations have solutions that are non-differentiable in the sense of ordinary derivatives and explain space and time with fractional dimensions. The illustrated examples with graphs present the details.