The Time-Fractional Perturbed Nonlinear Schrödinger Equation With Beta Derivative

In this article, we extract the diverse solitary wave solutions to the time-fractional perturbed nonlinear Schrödinger equation describing the dynamics of optical solitons travelling through nonlinear optical fibers. The nonlinear fractional differential equation is transformed into a nonlinear differential equation using a traveling wave transformation relating to the beta derivative. After that, the resulting equation is explained using the extended Riccati equation method. Abundant soliton and soliton-type solutions are extracted, comprising trigonometric and hyperbolic functions. The nature of the solutions varies qualitatively depending on distinct parameters. Additionally, graphical representations of the constructed solutions exhibit various physical forms, including kink, bell-shaped, periodic, anti-coupon etc. Moreover, the achieved solutions play a significant role in interpreting wave propagation studies and are essential for validating numerical and experimental findings in the fields of nonlinear optics, quantum mechanics, engineering, etc.