A New Study for the Investigation of Nonlinear Fractional Drinfeld–Sokolov–Wilson Equation.

In this paper, we present an idea of a new iterative procedure (NIP) to examine the approximate solution of the nonlinear fractional Drinfeld–Sokolov–Wilson (DSW) equation. We first use Mohand transform (MT) to the problem and obtain a recurrence relation without any assumption or restrictive variable. This relation is now very easy to handle and suitable for the study of the homotopy perturbation method (HPM). We observe that HPM produces the iterations in the form of convergence series that becomes very close to the precise solution. The fractional derivative is considered in the Caputo sense. We also demonstrate the graphical solution to show that NIP is a very simple, straightforward, and efficient tool for nonlinear problems of fractional derivatives. [ABSTRACT FROM AUTHOR]