Computational solution of a fractional generalization of the Schrödinger equation occurring in quantum mechanics

The object of this article is to present the solution of a fractional generalization of the Schrödinger equation of quantum mechanics in one dimension. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is obtained in a compact and computational form in terms of the H-function. A result given earlier by Debnath for the solution of a generalized Schrödinger equation is obtained in an explicit form in terms of the H-function, as a special case of our findings.