Abstract
•The proposed method is the based on δ-Homotopy Analysis Method (δ-HAM).•Illustrative examples are given to show the fast convergence and high accuracy of the proposed method.•The comparison of analytical solutions obtained from different derivative operators numerically and graphically.
In this paper, we extend the Burger’s equation to the time-fractional Burger’s equation based on different derivative operators as Yang-Abdel-Cattani, Atangana-Baleanu, Caputo-Fabrizio, and Liouville-Caputo. The analytical solutions for these different time-fractional Burger’s equation are determined by employing the δ-Homotopy Analysis Transform Method. Further, we study the comparison of analytical solutions obtained from different derivative operators numerically and graphically.