Local Fractional Yang-Laplace Variational Method for solving KdV Equation on Cantor Set

Abstract

In recent decades, to describe and solve physical problems,the theory of local fractional calculus has been used successfully. Inthis article, we apply the local fractional variational iteration transformmethod (LFVITM) to solve the local fractional linear & Nonlinear KdVequation on a Cantor set. Using this method, we obtained the nondifferentiableexact and approximate solutions for local fractional linearand Nonlinear KdV equations. It shows that the proposed method isan effective and useful method to performance for linear and Nonlinearproblems arising in science and engineering. We express that theLFVYTM method is a combination form the local fractional variationaliteration method and Yang-Laplace transform. Most of the solutionsobtained from this method in physics problems are series and converge quickly. To demonstrate the high accuracy and convergence of this procedure,some illustrative examples were used. Also, this method canreduce the amount of calculations compared to existing classical methods