Quantization of Singular Systems using Fractional Calculus

In this paper, we examined the theory of singular systems using fractional calculus. We quantized these systems using the fractional \textbf{WKB} approximation. We applied the Hamilton–Jacobi treatment for these systems. We obtained equations of motion. We constructed the fractional Hamilton–Jacobi partial differential equations (\textbf{FHJPDEs}) to obtain the action functions \textbf{S}. The action function enables us to obtain the wave function for these systems. We achieved that the quantum results agree with the classical results. Finally, we examined two mathematical examples to demonstrate the theory.