Abstract
•Numerical Comparison of Caputo and Conformable Derivatives.•Complex traveling wave solutions of the time-fractional Burgers-Fisher equation.•The use of sub-equation method to obtain new types of complex traveling wave solutions.•soliton solutions, exact complex traveling wave solutions and topological kink-type solitons.
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. L2 and L∞ 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.