Comparative dynamical analysis of exact and numerical solutions for the fractional telegraph equation

In this study, we investigate the fractional telegraph equation, a key nonlinear model for signal transmission, wave propagation, and complex dynamical systems in engineering. By combining the beta-derivative with [Formula: see text]-truncated transformations, we construct exact solutions and explore their dynamical traits through the enhanced modified extended tanh-expansion and unified methods, uncovering solitary, kink, bright, and periodic structures that embody the system’s nonlinearity. Finite-difference simulations accurately replicate these solutions with high fidelity, while bifurcation analysis maps stability and qualitative behavior across the parameter space. The seamless analytical-numerical framework reveals memory- and dispersion-driven dynamics, offering a reliable platform for future nonlinear fractional modeling.