Analysis of the nonlinear conformable Schrödinger equation with Kudryashov's refractive index using the generalized exponential rational function technique

This study applies the generalized exponential rational function technique to construct new optical soliton solutions of the nonlinear conformable Schrödinger equation with Kudryashov’s nonlinear refractive index governed by the quadrupled-power law and dual nonlocal nonlinearity. Various analytical solutions, including bright, dark, and wave solitons, are derived within the conformable fractional framework. The effects of the fractional-order parameter and temporal parameter on the obtained solutions are illustrated through contour, two-dimensional, and three-dimensional plots. The results reveal how fractional dynamics influence soliton structure, amplitude, and propagation behaviour. These findings contribute to a deeper understanding of pulse evolution and stability in nonlinear optical fibres and related photonic systems.