Searching the new exact wave solutions to the beta-fractional Paraxial nonlinear Schr_odinger model via three di?erent approaches

This research is concerned with some modernistic exact wave solutions of paraxial nonlinear Schrodinger model (PNLSM) along beta-fractional derivatives. The collected solutions can be executed in exposing this model in prominent form. The obtained results including trigonometric, hyperbolic trigonometric and exponential functions solutions. To obtain these solutions and the verification of achieved results, Mathematica tool is used. Three approaches, named as exp(a) function, extended (G'/G)- expansion and modified simplest equation approaches are employed to protect the results. The achieved results are also illustrated by two-dimensional (2D), three-dimensional (3D) and contour plots. The gained results are newer than the existing results in the literature and can also be fruitful for the development of model in future. The methods used in this paper are simple, reliable and accurate for solving the fractional nonlinear partial diffrential equations (NLPDEs).