A GENERALIZED METHOD AND ITS APPLICATIONS TO n-DIMENSIONAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN FRACTAL DOMAIN

Abstract

A generalized local fractional Riccati differential equation (LFRDE) method, which is a combination of the local fractional Riccati differential equation method and the transformed rational function approach, is presented to obtain the non-differentiable exact traveling wave solutions for n-dimensional fractional partial differential equations. In order to verify the effectiveness of the method, the seventh-order local fractional Sawada–Kotera–Ito equation, the local fractional sine-Gordon equation and the local fractional Kadomtsev–Petviashvili equation in fractal domain are first considered. The obtained results show that the presented method involving fractal special functions, are powerful and effective for obtaining exact solutions of nonlinear fractional partial differential equations in fractal domains.