Two distinct algorithms for conformable time-fractional nonlinear Schrödinger equations with Kudryashov’s generalized non-local nonlinearity and arbitrary refractive index

This paper investigates the application of the enhanced modified tanh expansion method and the Kudryashov method in deriving optical solutions for a conformable nonlinear Schrödinger equation. This equation includes Kudryashov’s arbitrary refractive index and incorporates two distinct nonlocal nonlinearities. The resulting optical solutions are expressed using a combination of exponential and hyperbolic functions, encompassing kink-type, mixed dark-bright, bright, bell-shaped, multi-bright, and wave solitons. Visualization of these solutions is provided through two-dimensional, three-dimensional, and contour plots to elucidate their characteristics. Furthermore, the behavior of these optical solutions is analyzed via illustrative graphs, considering different values of the time parameter and conformable order derivative. The proposed methods are posited as precise approaches for investigating optical solutions across various formulations of Schrödinger equations. The methods proposed in the paper offer precise approaches for studying and understanding the behavior of light in complex optical systems described by Schrödinger equations. This research contributes to advancing our knowledge of nonlinear optics and may have practical applications in fields such as telecommunications, laser technology, and optical signal processing.