University of Tabriz Computational Methods for Differential Equations 2345-3982 7 2 2019 04 01 Factorization method for fractional Schrödinger equation in D-dimensional fractional space and homogeneous manifold SL(2,c)/GL(1,c) 199 205 8592 EN Hossein Jafari Department of Mathematics, University of Mazandaran, Babolsar, Iran Jafar Sadeghi Physics Department, University of Mazandaran, P. O. Box 4716-95447, Babolsar, Iran Farzaneh Safari Department of Mathematics, University of Mazandaran, Babolsar, Iran Amos Kubeka Department of Mathematical Sciences, University of South Africa, P. O. Box 392, UNISA 0003, South Africa Journal Article 2017 02 24 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. https://cmde.tabrizu.ac.ir/article_8592_d070d098b3ad5fea48bfcf615203dbe1.pdf