Local fractional Laplace transform iterative method for solving Korteweg–de Vries equation with the local fractional derivative

Abstract

The local fractional Korteweg–de Vries equations were considered in this paper. Series solutions for the linear and nonlinear case were examined using the local fractional Laplace transform iterative method. This proposed method is the coupling of the local fractional Laplace transform with the new iterative method. The existence and uniqueness of the solutions is considered using the principle of mathematical induction. Furthermore, illustrative examples were considered and the graphs are shown. The results obtained in this study reveal the benefit of this method and provide valuable insight into the behavior of complex phenomena in a precise and efficient manner with less computational work and implementation ease.