Study of one-dimensional space-time fractional-order Burgers-Fisher and Burgers-Huxley fluid models

Abstract

The shifted Legendre collocation method is used to solve the one-dimensional nonlinear reaction-advection-diffusion equation having spatial and temporal fractional-order derivatives with initial and boundary conditions. The solution profiles of the normalized solute concentration of space-time fractional-order Burgers-Fisher and Burgers-Huxley equations are presented through graphs for different particular cases. The main purpose of the article is the graphical exhibition of the effect of the temporal, spatial fractional-order derivatives and the reaction term on the solution profile of the space-time fractional-order Burgers-Fisher and Burgers-Huxley equations. The other purpose of the article is the error estimation of the proposed method. A drive has been taken to validate the effectiveness of the proposed method through tabular presentation of comparison of numerical results with analytical results for the existing problems through convergence analysis. © 2019 John Wiley & Sons, Ltd.