In this paper, the sub-equation method is used to obtain new types of complex traveling wave solutions of the time-fractional Burgers-Fisher equation. In this work is to compare the exact complex traveling wave solutions of new types and the numerical solutions obtained by suitable transformations of Caputo and Conformable derivatives. Also, to discuss the advantages and disadvantages of those derivatives and a new initial condition was created by using the obtained solution and the numerical solutions of the equation were obtained by the finite difference method. A comparison of the numerical solutions with the obtained exact solution is made. $L_2$ and $L_{\infty }$ norm errors, absolute error values, Von Neumann stability analysis supporting this comparison are investigated. To consolidate the accuracy of the numerical results some tables and graphs are presented. For drawing complex mathematical operations and graphs, computer package programs are used.

在本文中，子方程法被用于获得时间分数阶Burgers-Fisher方程的新型复杂行波解。在这项工作中，将比较新型的精确复杂行波解和通过对Caputo和Conformable导数进行适当转换而获得的数值解。此外，为了讨论这些导数的优缺点，使用获得的解创建了一个新的初始条件，并通过有限差分法获得了方程的数值解。将数值解与获得的精确解进行比较。${\mathrm{大号}}_{\mathrm{2个}}$ 和 ${\mathrm{大号}}_{\infty }$范数误差，绝对误差值，冯·诺依曼稳定性分析均支持该比较。为了巩固数值结果的准确性，提供了一些表格和图表。为了绘制复杂的数学运算和图形，使用了计算机软件包程序。