Optical soliton analysis of an integrable wave packet envelope equation with conformable derivative

Abstract We study precise traveling wave solutions for a higher-order integrable wave packet envelope equation with conformable fractional derivatives for ultrashort pulse propagation with higher-order dispersion and nonlinear effects in optical fibers. The generalized exponential rational function technique is applied systematically to construct distinct families of analytical solutions: bright, dark, kink, and singular soliton structures. The dynamics of these optical pulses are shown in detailed 2D and 3D images of multiple conformable derivative orders, showing that fractional-order parameters play a major role in determining the wave propagation characteristics and stability. The solutions have provided unique information to design optical communication systems and control pulse dynamics in nonlinear photonic devices. This work presents a new, quantitative tool to perform complex analysis of fractional nonlinear wave interaction in modern fiber optic optical circuits, serving as a link between theory and practical integration in high-speed optical networks.