Exploring new exact solutions in the conformable time-fractional discrete coupled NLSE using a novel approach

This investigation focuses on the conformable time-fractional discrete coupled nonlinear Schrödinger system (CTFCDNLSEs). This system incorporates a fractional order represented as a conformable derivative. Through the application of the fractional transformation method (FTM), a set of novel analytical discrete solutions is derived. These solutions are characterized by an array of mathematical functions, including trigonometric, hyperbolic, and rational functions. Among these solutions, discrete fractional bright solitons, dark solitons, combined solitons, and periodic solutions stand out. To demonstrate the influence of the fractional-order parameter on the dynamics of fractional discrete solitons, graphical representations are provided. These findings are significant for exploring complex nonlinear discrete physical phenomena.