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Spatial non-locality of space-fractional viscoelastic equations of motion isstudied. Relaxation effects are accounted for by replacing second-order timederivatives by lower-order fractional derivatives and their generalizations. Itis shown that space-fractional equations of motion of an order strictly lessthan 2 allow for a new kind anisotropy, associated with angular dependence ofnon-local interactions between stress and strain at different material points.Constitutive equations of such viscoelastic media are determined. Explicitfundamental solutions of the Cauchy problem are constructed for some casesisotropic and anisotropic non-locality.

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy