q-Homotopy analysis method for solving the seventh-order time-fractional Lax’s Korteweg–de Vries and Sawada–Kotera equations

Abstract

This article presents exact and approximate solutions of the seventh order time-fractional Lax’s Korteweg–de Vries (7TfLKdV) and Sawada–Kotera (7TfSK) equations using the modification of the homotopy analysis method called the q-homotopy analysis method. Using this method, we construct the solutions to these problems in the form of recurrence relations and present the graphical representation to verify all obtained results in each case for different values of fractional order. Error analysis is also illustrated in the present investigation.