Investigating the truncated fractional telegraph equation in engineering: Solitary wave solutions, chaotic and sensitivity analysis

Communication systems, especially radio frequency and microwave systems are significant to global society. Optimizing these systems involves using the telegraph equation to determine power and signal losses. This equation is essential in theoretical, mathematical, and nonlinear research involving plasma physics, and is used to describe communication lines, the expansion of circulating blood pressure waves, and the random motion of one-dimensional bugs. This study investigates the dynamic behavior of the fractional telegraph equation with M-fractional derivative. The wave transformation is applied, and the model is transferred to an ordinary differential equation. Furthermore, two recently developed integration tools known as the generalized Arnous approach and modified F-expansion method have been adopted for analyzing the studied model. A variety of solitary wave solutions are extracted in different forms. Moreover, the fractional parametric effect has been observed graphically in various plots depicting wave dynamics. Another aspect of this study is to explore the telegraph by the chaotic and sensitivity analysis. For this purpose, the Galilean transformation is applied, and a variety of graphs in 2D phase portraits and time-series analyses have been sketched. The algorithms of the proposed techniques are outstanding allowing them to resolve exact soliton solutions in complex nonlinear structures with high precision in an efficient and effective manner. The results obtained may enhance the understanding of nonlinear system dynamics and validate current methods, significantly contributing to the fields of nonlinear science and wave phenomena. The analysis is expected to benefit numerous scientific models and related issues, making a significant contribution to nonlinear systems.