  In this paper the generalisation of previous author's formulation of
fractional continuum mechanics to the case of anisotropic non-locality is
presented. The considerations include the review of competitive formulations
available in literature. The overall concept bases on the fractional
deformation gradient which is non-local, as a consequence of fractional
derivative definition. The main advantage of the proposed formulation is its
analogical structure to the general framework of classical continuum mechanics.
In this sense, it allows, to give similar physical and geometrical meaning of
introduced objects.
