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In this article, we present new exact soliton solutions for the space-time fractional higher-order nonlinear Schrödinger equation, which describes the propagation of ultra-short pulses in nonlinear optical fibers. We apply a traveling wave transformation with the Beta derivative to convert the nonlinear fractional differential equation into a standard nonlinear differential equation. To find the exact analytical solutions, we implement the extended Riccati equation method, which led to a variety of soliton and soliton-like solutions, including trigonometric, hyperbolic, and rational functions. The graphical representations of these solutions show different physical forms, such as kink, periodic, bright bell, and dark bell structures. Additionally, we used planar dynamical systems theory to investigate the bifurcation phenomena in the derived system. A detailed sensitivity analysis was also performed on the dynamical system utilizing the Runge-Kutta method. These exact solitons play a vital role in understanding wave propagation and are essential for validating both numerical simulations and experimental findings in areas such as quantum mechanics, nonlinear optics and engineering.

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.