  A review of different approaches to describe anisotropic fractal media is
proposed. In this paper differentiation and integration non-integer dimensional
and multi-fractional spaces are considered as tools to describe anisotropic
fractal materials and media. We suggest a generalization of vector calculus for
non-integer dimensional space by using a product measure method. The product of
fractional and non-integer dimensional spaces allows us to take into account
the anisotropy of the fractal media in the framework of continuum models. The
integration over non-integer-dimensional spaces is considered. In this paper
differential operators of first and second orders for fractional space and
non-integer dimensional space are suggested. The differential operators are
defined as inverse operations to integration in spaces with non-integer
dimensions. Non-integer dimensional space that is product of spaces with
different dimensions allows us to give continuum models for anisotropic type of
the media. The Poisson's equation for fractal medium, the Euler-Bernoulli
fractal beam, and the Timoshenko beam equations for fractal material are
considered as examples of application of suggested generalization of vector
calculus for anisotropic fractal materials and media.
