Analytical solution of non-linear fractional Burger's equation in the framework of different fractional derivative operators

Abstract

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.