Stability, Bifurcation, and Traveling Wave Solutions to the Generalized Time-Fractional Burgers-Huxley Equation

In the field of mathematical sciences and engineering, traveling wave solutions play a crucial role in illustrating numerous nonlinear physical problems. Besides, fractional-order nonlinear partial differential equations demonstrate nonlinear physical phenomena more accurately. As a result, research investigations on fractional-order derivatives and fractional differential equations have been of recent interest. In our article, we investigate the generalized time-fractional Burgers-Huxley equation by means of the improved Bernoulli sub-equation function method and the concept of conformable fractional derivative. Additionally, we study the bifurcation analysis of the dynamical system as well as the stability of the equilibria. The study explores the combination of numerous parameters that provide distinct solutions. Here, the calculations and depiction of graphs are done by the mathematical software MAPLE. It is expected that the investigation will be helpful in describing nonlinear physical phenomena including shock waves, traffic flow, and acoustic transmission.