Effect of a new local derivative on space-time fractional nonlinear Schrödinger equation and its stability analysis

The study presented investigates the space-time fractional nonlinear Schrödinger equation, which is important in telecommunication industry, especially in optical fibers. The extended ( G ′ G 2 ) -expansion approach and the modified simple equation method are used to generate the soliton solutions of the model. A new local fractional derivative is implemented to investigate the fractional impacts on the model. Trigonometric, hyperbolic and rational functions with dark and periodic traveling tendencies are produced as results. Linear stability analysis is performed for the higher order nonlinear Schrödinger equation. Further, graphs are used to understand the fractional impacts of the local fractional derivative by assigning specific values to the fractional parameter.