https://doi.org/10.1140/epjs/s11734-021-00317-4
Regular Article
Laplace equations on the fractal cubes and Casimir effect
1
Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran
2
Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran
Received:
6
June
2021
Accepted:
25
October
2021
Published online:
9
November
2021
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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
