New optical wave solutions of M-fractional nonlinear Schr?dinger's complex hyperbolic model by an efficient method

In this paper, we succeed to obtain the new optical wave solutions to the truncated M-fractional (2+1)-dimensional nonlinear Schrodinger's complex hyperbolic model by utilizing the Sardar sub-equation method. The obtained solutions are in the form of trigonometric, hyperbolic and mixed form. These solutions have many applications in nonlinear optics, fiber optics, and other areas of physics and engineering where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by two-dimensional, three-dimensional and contour plots. The gained solutions are helpful for the further development of concerned model. Finally, this technique is simple, fruitful and reliable to handle the nonlinear PDEs.