Optical Soliton perturbation with fractional temporal evolution by extended modified auxiliary equation mapping

In this article we  discussed the analytical analysis of perturbed nonlinear fractional Schr$\ddot{o}$dinger equation with the help of our new introduced technique extended modified auxiliary equation mapping method(EMAEMM). By using this newly proposed technique we have found some new  and more general variety of exact traveling wave solutions which are collecting some kind of semi half bright, semi half dark, doubly periodic,  dark, combined, periodic, bright, half dark and half bright via three parametric values which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of plasma physics, quantum mechanics, biomedical problems, soliton dynamics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions via Mathematica 10.4 to get more understanding to observe the behavior of different new dynamical shapes of solutions.