We study fractional configurations in gravity theories and Lagrange
mechanics. The approach is based on Caputo fractional derivative which gives
zero for actions on constants. We elaborate fractional geometric models of
physical interactions and we formulate a method of nonholonomic deformations to
other types of fractional derivatives. The main result of this paper consists
in a proof that for corresponding classes of nonholonomic distributions a large
class of physical theories are modelled as nonholonomic manifolds with constant
matrix curvature. This allows us to encode the fractional dynamics of
interactions and constraints into the geometry of curve flows and solitonic
hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and
up-dated reference
