Analytical Study of Optical Solitons of the Space-Time Fractional Nonlinear Schrodinger Equations With Kudryashov's Refractive Index

In this article, we investigate the analytical optical solitons of two variants of the space-time fractional nonlinear Schrödinger equation, including Kudryashov's arbitrary refractive index.The models are formulated using the β-fractional derivative, which preserves the basic properties of classical calculus.The sine-Gordon expansion approach is used to originate exact and assorted soliton solutions, including complex, hyperbolic, and trigonometric forms.The obtained solutions describe a wide range of soliton structures, such as bright, dark, cuspon, kink, anti-kink, parabolic, and breather waves.A detailed parametric analysis shows that the fractional-order and nonlinear coefficients significantly affect the soliton amplitude, width, and propagation dynamics.The graphical simulations further confirm the stability and rich structural diversity of the solutions.The comparative results demonstrate that the sine-Gordon expansion approach is competent, accurate, and widely applicable.It also provides physically meaningful wave structures that are better than several existing techniques reported in the literature.The findings highlight the effectiveness of the proposed framework for modeling nonlinear pulse propagation in fractional optical fiber systems and related applications in nonlinear optics.