WKB Approximation with Conformable Operator

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 $\alpha=1$.