  The main goal of this work is to perform a nonolonomic deformation (Fedosov
type) quantization of fractional Lagrange geometries. The constructions are
provided for a (fractional) almost Kahler model encoding equivalently all data
for fractional Euler-Lagrange equations with Caputo fractional derivative. For
homogeneous generating Finsler functions, the geometric models contain quantum
versions of fractional Finsler spaces. The scheme can be generalized for
fractional Hamilton systems and various models of fractional classical and
quantum gravity. We conclude that the approach with Caputo fractional
derivative allows us to geometrize both classical and quantum (Fedosov type)
fractional regular Lagrange interactions.
