Analytic and Numerical Solutions ofTime-Fractional Linear SchrödingerEquation

Fractional Schrodinger equation is a basic equation in fractional quantum mechanics. In this paper, we consider both analytic and numerical solutions of time-fractional linear Schrodinger Equations. This is done via a proposed semi-analytical method upon the modification of the classical Differential Transformation Method (DTM). Some illustrative examples are used; the results obtained converge faster to their exact forms. This shows that this modified version is very efficient, and reliable; as less computational work is involved, even without given up accuracy. Therefore, it is strongly recommended for both linear and nonlinear time-fractional partial differential equations (PDEs) with applications in other areas of applied sciences, management, and finance.