An insight into the solitonic structure of two distinct fractional nonlinear Schrödinger models in optical fiber using conformable fractional derivative

The goal of this work was to use conformable fractional derivative sense to create some crucial solitary waves for two models of space–time fractional nonlinear Schrödinger equations. We use the unified solver approach to accomplish this goal in a fully unified way. This solution is robust, practical, dependable, and simple to use. The obtained solutions are extremely important for describing critical complicated phenomena in fractional quantum mechanics, optical fiber communications, and energy applications. Some simulations are provided to demonstrate the behavior of the obtained solutions when appropriate physical parameters are used. It was noted that by increasing the fractal factors, the nonlinear wave propagates with a changing phase and wave frequency. Our research may open up new possibilities for optical manipulation in practical applications. Finally, further fractional physical models can be solved using the suggested technique.