<p>This study innovatively focuses on the lossy nonlinear electrical transmission line model system. First, it conducts in-depth analysis using the Beta fractional derivative and inventively applies the unified <i>F</i>-expansion method to explore soliton solutions in Jacobian elliptic functions, revealing unique oscillation coupling phenomena. Second, it studies the two-dimensional dynamical system and phase portraits through skillful equation transformation, providing a visual tool for understanding the physical laws of the system. Third, it breaks previous restrictive conditions when constructing the Hamiltonian structure, more truly reflecting the physical conditions of transmission lines. Fourth, it expands the research on fractional-order changes in this model and discovers complex dynamic behaviors. Fifth, it adopts the Chebyshev spectral collocation method to solve numerical solutions, achieving high precision and low error. These novelly results enrich the understanding of the lossy nonlinear electrical transmission line model, lay a theoretical foundation for its applications in communication, power transmission, and related models, and hold broad prospects.</p>