Electrostatics in Fractal Geometry: Fractional Calculus Approach

Details Electrostatics in Fractal Geometry: Fractional Calculus Approach Electrostatics in Fractal Geometry: Fractional Calculus Approach

2011-08-31

arxiv.org/abs/1108.6171v1

Chaos, Solitons & Fractals 44 (2011) 335-341

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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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