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Laplace equations on the fractal cubes and Casimir effect

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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.

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Acknowledgements

This paper is dedicated to the memory of A.K.’s father Mohammad Khalili Golmankhaneh.

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Authors and Affiliations

  1. Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran

    Alireza Khalili Golmankhaneh

  2. Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran

    Safa Measoomy Nia

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  1. Alireza Khalili Golmankhaneh
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  2. Safa Measoomy Nia
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Khalili Golmankhaneh, A., Nia, S.M. Laplace equations on the fractal cubes and Casimir effect. Eur. Phys. J. Spec. Top. 230, 3895–3900 (2021). https://doi.org/10.1140/epjs/s11734-021-00317-4

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00317-4

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