EXPLORING THE β-FRACTIONAL TELEGRAPH EQUATION: INVESTIGATING THE OPTICAL SOLITARY WAVES, INTERACTION SOLUTIONS AND MULTISTABILITY ANALYSIS

The fractional telegraph equation is a significant modeling equation in nonlinear study. It describes various communication lines, including audio frequency such as telephone lines, direct current, high-frequency conductors, and low-frequency cable television. In this study, the dynamical behavior of telegraph equation with beta derivative is under consideration. We obtain various novel solutions like mixed, dark, bright, singular, combined, and bright-dark solitons with the usage of the newly introduced techniques known as modified generalized exponential rational function method and Riccati modified extended simple equation method and interaction solutions are under observation. Moreover, the multistablity analysis is also discussed with the Galilean transformation and two-dimensional phase portrait, time series analysis and Poincare maps are sketched. Additionally, we draw various graphs of the attained solutions that incorporate relevant parameters values to evaluate the physical characteristics of the solutions. Our analysis is expected to be beneficial for a significant number of scientific models.