  In this paper, the theory of the fractional singular Lagrangian systems is
investigated with second order derivatives. The fractional quantization for
these systems is examined using the WKB approximation. The Hamilton Jacobi
treatment can be applied for these systems. The equations of motion are
obtained. The Hamilton Jacobi partial differential equations are solved to
determine the action function. By finding the action function, the wave
function for these systems is constructed. We achieved that the quantum results
are agreement with the classical results. Besides, to demonstrate the theory;
two mathematical examples are examined.
