About Kepler's Third Law on fractal-time spaces


Khalili Golmankhaneh A.

Ain Shams Engineering Journal, vol.9, no.4, pp.2499-2502, 2018 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 9 Issue: 4
  • Publication Date: 2018
  • Doi Number: 10.1016/j.asej.2017.06.005
  • Journal Name: Ain Shams Engineering Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2499-2502
  • Keywords: Fractal calculus, Fractal triadic Cantor set, Fractal-time spaces, Kepler's Third Law, Local derivative on fractals
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, a mathematical model for fractal-time space is given involving Fα-calculus. Differential equations corresponding of the free fall motion and simple harmonic oscillator on fractal-time space are given and solved. Moreover, using scale transformation and invariant properties of physical laws we obtained the generalized Kepler's Third Law of motion on fractal-time space.