Abstract
Based on the work of Atangana-Baleanu [Open Math. 13 1 (2015)] we obtain new solutions of space-time fractional nonlinear Schrodinger equation, where (G'/G(2))-expansion and generalised Kurdyashov methods are suggested. The results obtained here include the hyperbolic, rational and trigonometric functions. Also, the behavior of the solutions is tested with changing of the values of fractional order, we can note that the obtained solutions reduced back to the results reported previously to the normal case i.e, alpha = 1 and beta = 1, that we can say that the fractional order can be used as a controlling parameter of the system solutions. We can see from the obtained results the all solutions almost same, the difference only on the initial point, where we can say that the proposed methods and the steps to find the solutions are more efficient and accurate.