Yokus, AsifYavuz, Mehmet2024-02-232024-02-2320211937-16321937-1179https://doi.org/10.3934/dcdss.2020258https://hdl.handle.net/20.500.12452/16137In this paper, we investigate some analytical, numerical and ap-proximate analytical methods by considering time-fractional nonlinear Burger- Fisher equation (FBFE). (1/G')-expansion method, finite difference method (FDM) and Laplace perturbation method (LPM) are considered to solve the FBFE. Firstly, we obtain the analytical solution of the mentioned problem via (1/G')-expansion method. Also, we compare the numerical method solutions and point out which method is more effective and accurate. We study trun-cation error, convergence, Von Neumann's stability principle and analysis of linear stability of the FDM. Moreover, we investigate the L-2 and Loo norm errors for the FDM. According to the results of this study, it can be concluded that the finite difference method has a lower error level than the Laplace per-turbation method. Nonetheless, both of these methods are totally settlement in obtaining efficient results of fractional order differential equations.eninfo:eu-repo/semantics/openAccessFinite Difference MethodLaplace Perturbation MethodLinear StabilityAnalytical SolutionCaputo Fractional DerivativeNonlinear Time-Fractional Burger-Fisher EquationArticle147259126062-s2.0-85109168248Q2WOS:000663083300007Q210.3934/dcdss.2020258