  We derive basic equations of electromagnetic fields in fractal media which
are specified by three indepedent fractal dimensions {\alpha}_{i} in the
respective directions x_{i} (i=1,2,3) of the Cartesian space in which the
fractal is embedded. To grasp the generally anisotropic structure of a fractal,
we employ the product measure, so that the global forms of governing equations
may be cast in forms involving conventional (integer-order) integrals, while
the local forms are expressed through partial differential equations with
derivatives of integer order but containing coefficients involving the
{\alpha}_{i}'s. First, a formulation based on product measures is shown to
satisfy the four basic identities of vector calculus. This allows a
generalization of the Green-Gauss and Stokes theorems as well as the charge
conservation equation on anisotropic fractals. Then, pursuing the conceptual
approach, we derive the Faraday and Amp\`ere laws for such fractal media,
which, along with two auxiliary null-divergence conditions, effectively give
the modified Maxwell equations. Proceeding on a separate track, we employ a
variational principle for electromagnetic fields, appropriately adapted to
fractal media, to independently derive the same forms of these two laws. It is
next found that the parabolic (for a conducting medium) and the hyperbolic (for
a dielectric medium) equations involve modified gradient operators, while the
Poynting vector has the same form as in the non-fractal case. Finally,
Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In
all the cases, the derived equations for fractal media depend explicitly on
fractal dimensions and reduce to conventional forms for continuous media with
Euclidean geometries upon setting the dimensions to integers.
