A NEW FRACTAL TRANSFORM FOR THE APPROXIMATE SOLUTION OF DRINFELD–SOKOLOV–WILSON MODEL WITH FRACTAL DERIVATIVES

Abstract

This study examines the development of a novel approach known as the fractal Elzaki transform method (F[Formula: see text]TM) to investigate the approximation solution of the nonlinear fractal Drinfeld–Sokolov–Wilson (NFDSW) model. We adopt He’s fractal derivative to change the fractal model into its differential parts and then apply the Elzaki transform to obtain the recurrence relation. We utilize the framework of homotopy perturbation method to handle the nonlinear components of this recurrence relation and thus we can obtain the successive iterations very easily. The derived findings are performed in the form of series and the rate of convergence shows the remarkable solutions due to its fast convergence. The numerical example illustrates that F[Formula: see text]TM is very easy to implement and a fascinating tool for fractal models.