Electrostatics in fractal geometry: Fractional calculus approach

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.

► The electric field in a composite dielectric with a fractal charge distribution is observed.
► The observation is based on a relation between fractal geometry and fractional calculus.
► The mathematical construction is relevant to studying electrostatics in real composites.