Fractional dynamics and optical soliton propagation in mono-mode fibers via the Fokas system

The research investigates pulse propagation through mono-mode optical fibers using the fractional Fokas system by integrating the conformable fractional calculus with the generalized Riccati-Bernoulli sub-ODE method along with Bäcklund transformation. The figures demonstrate perturb kink soliton profiles using 2D plots for fractional-order parameter ($$\alpha$$) together with 3D plots for integer-order conditions to depict the solutions dynamic nature. The model demonstrates its physical operation range through different initial condition analyses which increases its potential for widespread application. The derived solutions demonstrate the ability of the combined approach to be an effective mathematical methodology that addresses various types of nonlinear wave phenomena. The optical solitons enable researchers to study energy transport and diffusion mechanisms in fractional-order systems specifically regarding pulse propagation in optical communication networks.