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.