  In this paper, the WKB method is extended to be applicable for conformable
Hamiltonian systems where the concept of conformable operator with fractional
order $\alpha$ is used. The WKB approximation for the $\alpha$-wavefunction is
derived when the potential is slowly varying in space. The paper is furnished
with some illustrative examples to demonstrate the method. The quantities of
the conformable form are found to be inexact agreement with traditional
quantities when $\alpha=1$.
