Electrostatics in Fractal Geometry: Fractional Calculus Approach
  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. 
Emmanuel Baskin and Alexander Iomin
cond-mat.stat-mech cond-mat.mes-hall physics.optics