Construction of soliton solutions for the fractional Gilson–Pickering model via diverse analytical schemes

Abstract

The present manuscript investigates novel soliton wave solutions of the fractional Gilson–Pickering model by systematically employing four efficient analytical methods, facilitated through the computational capabilities of the Mathematica software. In optics, the fractional Gilson–Pickering model is used to describe the propagation of nonlinear optical waves and pulse dynamics in dispersive optical media. Its fractional form is particularly important for modeling memory effects, nonlocal interactions, attenuation, and anomalous dispersion in optical fiber systems and complex photonic structures. The underlying model is rigorously reformulated using the conformable fractional derivative operator, enabling the derivation of a rich set of exact solutions in diverse functional forms, including hyperbolic, trigonometric, exponential, and rational expressions. These solutions are further visualized through comprehensive 2-dimensional and 3-dimensional plots, providing clear insights into the physical behaviors and dynamical properties of the fractional system. The study not only demonstrates the versatility and effectiveness of the employed analytical techniques but also establishes a valuable framework for exploring and validating soliton structures in a wide range of fractional nonlinear models. Consequently, the proposed methodology represents a significant contribution to the advancement of mathematical tools for the analysis of complex phenomena in nonlinear science and applied physics, offering both theoretical depth and practical computational utility.