Abstract
•A new analytic solution of fractional coupled Ramani equation is described.•Q-homotopy analysis transform method is employed.•The present method gives highly approximate results with a few iterations.
A new analytic solution of fractional coupled Ramani equation (sixth-order coupled Ramani equation) is described. Q-homotopy analysis transform method (q-HATM) technique is proved to be a useful tool for generating the solution. The convergence of the q-HATM is controlled by auxiliary parameters ℏ and n. We compared the solutions with the exact solutions and some analytical methods to show the reliability of the method. The present method gives highly approximate results with a few iterations. The new results we have obtained may be meaningful in explaining some problems in Soliton theory.