Abstract
A new approximate solution of the fractional nonlinear integrable single sixth order Drinfeld–Sokolov–Satsuma–Hirota (DSSH) equation is introduced and depicted. The q‐homotopy analysis transform method (q‐HATM) is a powerful algorithm to solve such problem. The proposed algorithm offers an approximate solution that is very close to the exact solution while avoiding the complexity that exists in many other methods. With the help of Banach's fixed‐point theory, the uniqueness theorem and convergence analysis of the anticipated issue are discussed. The normal frequency for the fractional solution to this problem differs by the difference in the fractional derivative.