WKB approximation with conformable operator

In this paper, the Wentzel?Kramers?Brillouin (WKB) method is extended to be applicable for conformable Hamiltonian systems, where the concept of conformable operator with fractional order is involved. The WKB approximation for the -wave function is derived for potentials which slowly vary in space. Some illustrative examples to demonstrate the method are presented. The quantities of the conformable form are found to be in exact agreement with the corresponding traditional quantities when .