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 V(d) similar to 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. (C) 2011 Elsevier Ltd. All rights reserved.