Probability Structure of Time Fractional Schrodinger Equation

We consider the motion of a particle under the influence of a real potential within the framework of time fractional Schrodinger equation in 1 + 1 dimensions. For the basis states we obtain a simple expression for the probability current equation. In the limit where the order of fractional derivative is close to unity we find a fluctuating probability density for the basis states. We also provide a compact expression for the time rate of change of the probability density in this case. For the special case where the order of fractional derivative is equal to 1/2 we compute the probability density.