In this article, the influence of time discreteness on the transition coefficients is investigated within the framework of time fractional development of quantum systems which has been developed recently by the present authors . In this formalism, fractional mathematics which is a powerful tool to study the non-Markovian and non-Gaussian properties of physical processes is used in order to obtain time fractional evolution operator and transition probability. They are given in terms of Mittag-Leffler function which plays an important role in the mathematical structure as well as the physical interpretation of the phenomena under investigation. In order to place the presented formalism on a concrete basis, historical Stern-Gerlach experiment has been revisited with the purpose of studying transition coefficients which have a non-Markovian feature. The effect of the time fractionalization has been clearly illustrated in the figures via fractional derivative order (C) 2010 Elsevier Ltd. All rights reserved.