Initial Value Problem for a Caputo Space-time Fractional Schrodinger Equation for the Delta Potential

In this paper, we investigate the initial value problem for a Caputo space-time fractional Schrodinger equation for the delta potential. To solve this equation, we use the joint Laplace transform on the spatial coordinate and the Fourier transform on the time coordinate. Finally, the wave function and the time dependent energy eigenvalues are obtained for a particle which is subjected to the delta potential.