  This paper is about the fractional Schr\"{o}dinger equation (FSE) expressed
in terms of the quantum Riesz-Feller space fractional and the Caputo time
fractional derivatives. The main focus is on the case of time independent
potential fields as a Dirac-delta potential and a linear potential. For such
type of potential fields the separation of variables method allows to split the
FSE into space fractional equation and time fractional one. The results
obtained in this paper contain as particular cases already known results for
FSE in terms of the quantum Riesz space fractional derivative and standard
Laplace operator.
