This current research is about some new exact wave solutions to the generalized ( 1 + 1)-dimensional unstable nonlinear Schrodinger equation with novel truncated M-fractional derivative. The obtained solutions may be applied in the demonstration of this model in some better way. The novel derivative operator is applied to study the aforementioned model. These solutions are in the form of dark, bright and other solutions with certain conditions. The achieved solutions are also verified by using the MATHEMATICA software. Modified integration method, extended Jacobi's elliptic expansion functions method (EJEEFM) is utilized to secure the aforesaid solutions. These exact solitons suggest that this method are effective, straight forward and reliable as compare to other methods.