On cylindrical model of electrostatic potential in fractional dimensional space

The Laplace's equation in a fractional dimensional space describes the electrostatic potential inside fractal media in the framework of fractal continuum models. An exact solution of the Laplace's equation for cylindrical coordinate system in a space having fractional (non-integer) dimensions is derived and discussed. The discussion is divided into different cases. These cases are based on the values of parameters describing the order of fractional dimensional space and the parameter used to describe azimuthal and/or radial dependency of the potential. A coaxial cable with constant potential and filled with a fractional dimensional space is also solved as an example.