Many real-world phenomena such as nerve pulse transmission, fluid transport, and chemical kinetics are modeled using nonlinear partial differential equations with time-fractional derivatives. Among them, the time-fractional Burgers-Huxley equation plays a significant role due to its ability to capture both diffusion and reaction mechanisms with memory effects. Solving such equations in higher dimensions is highly challenging and calls for efficient analytical approaches. In this work we present a technique for handling the time-fractional Burgers-Huxley equation up to k-dimensions by employing Laplace transform based homotopy perturbation method (LT-HPM). The LT-HPM is adopted based on its advantage in dealing with nonlinear terms and simplify the solution process by converting fractional derivatives into more manageable expressions. Unlike other hybrid approaches, LT-HPM is less computational complex and provides rapid convergent series solutions without requiring any linearization or restrictive assumptions. To showcase the effectiveness of this approach, we solve a pair of examples: a 2-D case and a 3-D case. The obtained results confirm that LT-HPM is accurate and powerful in tackling complex nonlinear PDEs in higher dimensions.
Kumari et al. (Thu,) studied this question.