Factorization method for fractional Schrödinger equation in D-dimensional fractional space and homogeneous manifold SL(2,c)/GL(1,c)

In this paper, we consider a $D$-dimensional fractional Schr"odinger equation with a Coulomb potential. By using the associated Laguerre and Jacobi equations, we obtain the wave function and energy spectrum and this then enable us to separate this equation in terms of the radial and angular momentum parts respectively. Also the associated Laguerre and Jacobi equations makes it possible to further factorize the $D$-dimensional fractional Schr"odinger equation such that the resulting equations can be expressed in terms of the first order operators which are basically raising and lowering operators.