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

Fractional calculus is a branch of classical mathematics, which deals with the generalization of fractional order derivative and integral operator. Recently, a great deal of research has been carried out on the use of fractional calculus to study the phenomena associated with fractal structures and processes. Fractals have a fractional dimension and occur naturally in non-linear and imbalanced phenomena in various forms and contexts. In recent years, various types of derivatives and fractional and fractal calculus have been proposed by many scientists and have been extensively utilized. Measurements are localized in physical processes, and local fractional calculus is a useful tool for solving some type of physical and engineering problems. In this article, we applied the local fractional Yang-Laplace variational for solving the local fractional linear and nonlinear KdV equation on a Cantor set within local fractional derivative. we emphasize on the LFYLVM method which is a combination form of local fractional variational iteration method and Yang-Laplace transform. The non-differentiable exact and approximate solutions are obtained for kind of local fractional linear and nonlinear KdV equations. Most of the solutions obtained from this method are obtained in series form that converge rapidly in physical problems. Illustrative examples are included to demonstrate the high accuracy and convergence of this algorithm It is shown that the used method is an efficient and easy method to implement for linear and nonlinear problems arising in science and engineering.