This paper provides a thorough investigation of the new Kudryashov method for obtaining optical solutions relevant to a time-fractional nonlinear Schrödinger equation (NLSE) modified with Kudryashov’s advanced refractive index (RI) formulation. The resulting optical solutions are indicated by their formulation through exponential and hyperbolic functions. To show the significance of these optical solutions, a variety of 2D, 3D and contour visual representations are presented. Additionally, graphical representations are utilised to reveal the dynamic properties of these diverse optical solutions in response to changes in the time parameter and order. The implications of these findings are substantial for their potential application in the propagation of pulses within optical fibres and other areas of physics. Moreover, the model is well-suited for investigating the polarisation of solitons in birefringent fibres. The methodology proposed in this manuscript is suggested to serve as an accurate tool for exploring optical solutions across a range of NLSEs, including both fractional and integer orders. The optical solitons described in this work are expected to have promising applications in the field of nonlinear optics, opening up new avenues for the study and utilisation of soliton dynamics.
