Mathematical and numerical study of existence of bifurcations of the generalized fractional Burgers-Huxley equation

Abstract

The generalized Burger-Huxley equation (gBH) with fractional derivative is considered to provide some characteristics of memory embedded into the system. The modified model is analyzed analytically by using generalized fractional Taylor series and the residual functions. This technique is known as the residual power series method. In some cases of the gBH, we observe that when the value of memory index is close to zero, the solutions bifurcate and produce a wave-like pattern.