Analytical Solutions of the Fractional Derivative Chen–Lee–Liu Equation

This paper investigates a Schrödinger-type fractional-order nonlinear equation known as the Chen–Lee–Liu equation. The fractional properties of the model are described by means of the reduced M-fractional derivative. Using a traveling-wave ansatz and a change in variables, the original fractional partial differential equation is reduced to an ordinary differential equation, which is then solved analytically. The obtained solutions represent soliton-type nonlinear wave structures and depend on the model parameters. A detailed analysis of the influence of the fractional-order parameter α on the amplitude, propagation velocity, and spatial localization of the solutions is performed. It is found that decreasing α leads to increased dissipative effects and an expansion of the wave propagation region. A comparative study of the classical case (α=1) and the fractional-order case (α<1) reveals significant differences in the solution dynamics. Numerical simulations confirm the stability of the obtained solitons. The results demonstrate the effectiveness of fractional-order models in describing complex nonlinear processes that involve memory and dissipation.