Abstract

This article introduces and illustrates a novel approximation to the compound KdV-Burgers equation. For such a challenge, the q-homotopy analysis transform technique (q-HATM) is a potent approach. The suggested procedure avoids the complexity seen in many other methods and provides an approximation that is extremely near to the exact solution. The uniqueness theorem and convergence analysis of the expected problem are explored with the aid of Banach's fixed-point theory. Through a difference in the fractional derivative, the normal frequency for the fractional solution to this issue changes. All of the discovered solutions are illustrated in the figures and tables.