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Electrostatics in fractal geometry: Fractional calculus approach

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  • Baskin, Emmanuel
  • Iomin, Alexander

Abstract

An electric field in a composite dielectric with a fractal charge distribution is obtained in the spherical symmetry case. The method is based on the splitting of a composite volume into a fractal volume Vd∼rd with the fractal dimension d and a complementary host volume Vh=V3−Vd. Integrations over these fractal volumes correspond to the convolution integrals that eventually lead to the employment of the fractional integro-differentiation.

Suggested Citation

  • Baskin, Emmanuel & Iomin, Alexander, 2011. "Electrostatics in fractal geometry: Fractional calculus approach," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 335-341.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:4:p:335-341
    DOI: 10.1016/j.chaos.2011.03.002
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    References listed on IDEAS

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    1. Weiss, George H. & Havlin, Shlomo, 1986. "Some properties of a random walk on a comb structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 134(2), pages 474-482.
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    Cited by:

    1. Balankin, Alexander S., 2020. "Fractional space approach to studies of physical phenomena on fractals and in confined low-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Méndez, Vicenç & Iomin, Alexander, 2013. "Comb-like models for transport along spiny dendrites," Chaos, Solitons & Fractals, Elsevier, vol. 53(C), pages 46-51.

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