Initial value problem for a Caputo space-time fractional Schrödinger equation for the delta potential

Abstract

In this paper, we consider a Caputo space-time fractional Schrodinger equation for the delta potential. To solve the equation, we use the ¨ joint Laplace and Fourier transforms on the spatial and time coordinates, respectively. After applying the integral transformations, we use the special initial and boundary physical conditions obtained by trial and error; these special initial conditions involve considering the initial spatial wave function in terms of the Mittag-Leffler function. Consequently, using the fractional calculus, we obtain the wave functions and corresponding eigenvalues. Finally, to verify the solution, we recover the standard case corresponding to α → 1 and β → 1.