Electrostatics in Fractal Geometry: Fractional Calculus Approach

Emmanuel Baskin; Alexander Iomin

doi:10.1016/j.chaos.2011.03.002

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arXiv · 1108.6171

Electrostatics in Fractal Geometry: Fractional Calculus Approach

Emmanuel Baskin·Alexander Iomin

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Abstract

The electrostatics properties of composite materials with fractal geometry are studied in the framework of fractional calculus. 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 $V_d\sim r^d$ with the fractal dimension $d$ and a complementary host volume $V_h=V_3-V_d$. Integrations over these fractal volumes correspond to the convolution integrals that eventually lead to the employment of the fractional integro-differentiation.

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Emmanuel Baskin, Alexander Iomin. 2011-08-31. Electrostatics in Fractal Geometry: Fractional Calculus Approach. https://doi.org/10.1016/j.chaos.2011.03.002

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