New optical soliton solutions to nonlinear Schrödinger equation with fractional temporal evolution having parabolic and dual power law nonlinearities

In this work, we provide the analytical solutions to nonlinear Schrödinger equation with parabolic law and dual power-law nonlinearities including the conformable derivative. The different techniques considered here are the new mapping, the unified Riccati equation and the new modified sub-ODE technique. The implemented techniques have led to obtain a variety of soliton structures, including the bright, kink, dark, singular soliton, and periodic waves. Some graphical depictions are given to visualize the propagation characteristics of different kinds of soliton solutions. Additionally, technical criterion for occurrence of these optical solitons is provided. The results may be useful in the physics and engineering fields of fiber optics.