  Application of the fractional calculus to quantum processes is presented. In
particular, the quantum dynamics is considered in the framework of the
fractional time Schr\"odinger equation (SE), which differs from the standard SE
by the fractional time derivative: $\frac{\prt}{\prt t}\to
\frac{\prt^{\alpha}}{\prt t^{\alpha}}$. It is shown that for $\alpha =1/2$ the
fractional SE is isospectral to a comb model. An analytical expression for the
Green functions of the systems are obtained. The semiclassical limit is
discussed.
