Non-polynomial Spline Method for Time-fractional Nonlinear Schrödinger Equation

In this paper, we propose a quintic non-polynomial spline approach coupled with $L1$ formula for the numerical treatment of time-fractional nonlinear Schrodinger equation. The unconditional stability is proved by Fourier method for $0 , where $\gamma$ is the order of the Caputo time-fractional derivative. The efficiency of the proposed numerical scheme is illustrated by numerical experiments, where the simulation results indicate better performance over previous work in the literature.