Investigation of the Time-Fractional Generalized Burgers–Fisher Equation via Novel Techniques

Numerous applied mathematics and physical applications, such as the simulation of financial mathematics, gas dynamics, nonlinear phenomena in plasma physics, fluid mechanics, and ocean engineering, utilize the time-fractional generalized Burgers–Fisher equation (TF-GBFE). This equation describes the concept of dissipation and illustrates how reaction systems can be coordinated with advection. To examine and analyze the present evolution equation (TF-GBFE), the modified forms of the Adomian decomposition method (ADM) and homotopy perturbation method (HPM) with Yang transform are utilized. When the results are achieved, they are connected to exact solutions of the (Formula presented.) order and even for different values of (Formula presented.) to verify the technique’s validity. The results are represented as two- and three-dimensional graphs. Additionally, the study of the precise and suggested technique solutions shows that the suggested techniques are very accurate.