Kang‐Le Wang
In this work, the fractional Kaup–Newell system is investigated, which is an important model in optical fibers. Some new soliton solutions are successfully derived based on two excellent mathematical approaches, which are called [Formula: see text]-expansion method and new fractional auxiliary equation method. The variational principle of the fractional Kaup–Newell system is established via a semi-inverse method, and the bright soliton and periodic wave solutions are obtained. In order to further illustrate the physical characteristics of these derived soliton solutions and the influence of the fractional order values on the soliton solutions, these solutions are described by plotting the corresponding three-dimensional, two-dimensional and density graphs with appropriate parameter values and different fractional order values. In addition, a plane dynamic system is constructed by adopting the Galilean transformation, and the bifurcation analysis, chaotic behavior and sensitivity analysis are discussed. These newly obtained results contribute to a deeper theoretical understanding of fractional soliton dynamics and support its practical applications in nonlinear optics and engineering physics.