New solitary wave solutions for the triplet coupled nonlinear Schrödinger system incorporating fractional effects

New traveling wave solutions for the nonlinear fractional Schrödinger equation (FSE), obtained using conformable fractional derivatives, are presented in this paper. Despite extensive research on classical and fractional Schrödinger models, a systematic development of accurate traveling wave solutions employing conformable operators in conjunction with effective symbolic approaches remains lacking. To bridge this gap, we employ a Hamiltonian-based technique, a variational formulation via the Ritz method, and the modified Sardar subequation method. The fractional governing model is reduced to a nonlinear ordinary differential equation through a complex traveling wave transformation, which is analytically solved to yield new families of solutions. Two- and three-dimensional graphical representations of the solution's physical properties are presented, emphasizing the wave dynamics of the proposed fractional model.