Electrostatics in Fractal Geometry: Two Examples of Fractional Calculus 

Electrostatics in Fractal Geometry: Two Examples of Fractional
Calculus Electrostatics properties of composite materials, with
fractal geometry are studied in the framework of the fractional
calculus. An electric field in a composite dielectric with a fractal
charge distribution is obtained for different realizations of the
fractal geometry. The method is based on splitting of a composite
volume into a fractal volume $V_d?sim r^d$ of a fractal dimension $d$
and a complementary host volume $V_3-V_d$. Integrations over these
fractal volumes correspond to the convolution integrals and,
eventually, to employment of the fractional integro-differentiation.