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 M-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 systems nonlinearity. Finite-difference simulations accurately replicate these solutions with high fidelity, while bifurcation analysis maps stability and qualitative behaviour across the parameter space. The seamless analytical-numerical framework reveals memory- and dispersion-driven dynamics, offering a reliable platform for future nonlinear fractional modelling.
In this study, we investigate the fractional telegraph equation, a key nonlinear model for signal transmission, wave propagation, and complex dynamical systems in engineering.
A key research challenge in modern cryptography is the construction of robust nonlinear components that simultaneously achieve high nonlinearity, resistance to linear and differential…
In this paper, we investigated higher-order smooth positon and breather-positon solutions of the Kuralay equation. Starting from the associated Lax pair, we constructed an explicit N-fold Darboux…