A Coupling Method of Local Fractional Variational Iteration Method and Yang-Laplace Transform for Solving Laplace Equation on Cantor Sets

摘要

A user friendly algorithm based on new local fractional variational iteration transform method (LFVITM) is proposed to solve local fractional Laplace equation on Cantor sets within local fractional derivative. Further, the same problem is solved by local fractional variational iteration method and local fractional Adomian decomposition method. The results obtained by the three methods are in agreement and hence this technique may be considered an alternative and efficient method for finding approximate solutions of both linear and nonlinear fractional differential equations. The LFVITM is a combined form of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.