Laplace equations on the fractal cubes and Casimir effect

Khalili Golmankhaneh A., Nia S. M.

European Physical Journal: Special Topics, vol.230, no.21-22, pp.3895-3900, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 230 Issue: 21-22
  • Publication Date: 2021
  • Doi Number: 10.1140/epjs/s11734-021-00317-4
  • Journal Name: European Physical Journal: Special Topics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC
  • Page Numbers: pp.3895-3900
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we have generalized fractal calculus on fractal Cantor cubes. The mass function on fractal Cantor cubes is defined. Then, we use the mass function to define integral staircase function on fractal Cantor cubes. Using the integral staircase function, the fractal derivatives and integrals for a function with fractal Cantor cubes are defined. Fractal Laplace equations are suggested and their solutions are plotted to show more details. As application, Casimir effect is modeled by fractal Laplace equation.