Modeling the fractional non-linear Schrödinger equation via Liouville-Caputo fractional derivative

In this paper the modified homotopy analysis transform method is applied to obtain approximate analytical solutions of the time-fractional non-linear Schrödinger equation. The fractional derivative is described in the Liouville-Caputo sense. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. New exact solutions are constructed under constraint conditions. Employing theoretical parameters, we present some numerical simulations.