  The goal of this paper is to encode equivalently the fractional Lagrange
dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo
derivative generalized for nontrivial nonlinear connections (N-connections)
originally introduced in Finsler geometry, with further developments in
Lagrange and Hamilton geometry and, in our approach, with fractional
derivatives. For fundamental geometric objects induced canonically by regular
Lagrange functions, we construct compatible almost symplectic forms and linear
connections completely determined by a "prime" Lagrange (in particular,
Finsler) generating function. We emphasize the importance of such constructions
for deformation quantization of fractional Lagrange geometries and applications
in modern physics.
