In this research work, we elucidate the dynamical behavior of optical solitons to the generalized (1 + 1)-dimensional unstable space–time fractional nonlinear Schrödinger (gf-UNLS) model emerging in nonlinear optics. A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, (\(\frac{G^{\prime }}{G^2}\))-expansion function method and the modified direct algebraic method). Besides, we also secure singular periodic wave solutions with unknown parameters. All the reported solutions are verified by putting back to the original equation through soft computation Mathematica. The modulation instability analysis for the given nonlinear Schrödinger model is also observed. The outcomes reveal that the governing model theoretically possesses immensely rich structures of optical soliton solutions. The physical characterization of some obtained results are figured out graphically in 3D, and their corresponding contour profiles by using different scales of parameters to clarify and visualize the physical features of the problem.

在这项研究工作中，我们阐明了光学孤子对非线性光学中出现的广义（1 + 1）维不稳定时空分数非线性薛定谔（gf-UNLS）模型的动力学行为。通过使用三种有效的数学工具，即扩展正弦波，提取各种非线性动态光学孤子结构以不同的形状，如双曲线、三角波和平面波解，包括一些特别已知的孤波解，如亮、暗、奇异和组合孤子。戈登方程展开法，( \(\frac{G^{\prime }}{G^2}\))-扩展函数方法和改进的直接代数方法)。此外，我们还确保了具有未知参数的奇异周期波解。所有报告的解都通过软计算 Mathematica 回到原始方程来验证。还观察到给定非线性薛定谔模型的调制不稳定性分析。结果表明，该控制模型理论上拥有极其丰富的光学孤子解结构。一些获得的结果的物理特征在 3D 中以图形方式计算出来，并通过使用不同尺度的参数来阐明和可视化问题的物理特征。