A newly constructed numerical approximation and analysis of Generalized fractional Burger-Huxley equation using higher order method

Abstract

In this manuscript, the collocation approach using the higher order extended cubic B-spline (ECBS) as the basis function is efficiently used to numerically solve the generalized time fractional Burger-Huxley equation (TFBHE). The Burger-Huxley equation is a widely studied nonlinear partial differential equation that models the propagation of nerve impulses in excitable systems such as the neurons in the brain. The time fractional versions of the Burger-Huxley equation (BHE), which incorporate fractional derivatives in time direction to model the anomalous diffusion, reaction mechanism, and memory effects observed in many physical and biological systems. The θ−weighted technique and the Atangana–Baleanu operator are employed to discretize the equation. The higher order EBCS method is used in space direction. The stability and convergence analysis are also presented. Numerous examples are carried out to show the validity of the technique. The graphical representations and computed results are observed the good agreement with the literature.

Keywords

• Time fractional reaction–diffusion model
• B-spline basis
• Atangana–Baleanu derivative