On Generalized Fractional Spin, Fractional Angular Momentum, Fractional Momentum Operators in Quantum Mechanics

In this study, we have extended the idea of fractional spin introduced recently in literature based on two orders fractional derivative operator. Generalizations of the fractional spin, the fractional angular momentum and the fractional momentum operators were obtained. The theory is characterized by a noncommutativity between the generalized fractional angular momentum and the fractional Hamiltonian. We have derived the corresponding fractional Schrodinger equation and we have discussed its implications on the problems of a free particle and a particle moving in an infinite well potential. Enhancements of their corresponding energies levels and ground energies were observed which are in agreement with phenomenological theories such as noncommutative quantum mechanics.