Investigation of Fractal Fractional nonlinear Drinfeld–Sokolov–Wilson system with Non-singular Operators

Abstract

The aim of this article is to study the Drinfeld–Sokolov–Wilson equation considered in fractal-fractional sense with exponential decay and Mittag-Leffler type kernels. The Laplace transform combined with Adomian decomposition method is used to calculate the general solution of the system in series form. The convergence of the obtained series solution is also presented. For validity of our results, we consider a numerical example with suitable initial conditions. The results reveal that by decreasing fractal parameter enhances the amplitude of the soliton solution of the system. Moreover, decreasing fractional parameter, rapidly increases the amplitude of solitary wave of the system. We also observed that for small value of time t, the wave solutions of the system are very close to each other, while increasing in time t enhances the system when one of the parameters fractional or fractal is equal to one. We also studied the error analysis of the system reveals that the absolute error decreases as spatial variable x increases at small time t, while, increase in iterations, reduces the absolute error in the system.