New exact solutions of the local fractional (3+1)-dimensional Kadomstev-Petviashvili equation

Abstract

Aided by the local fractional derivative, we present a new local fractional (3+1)-di?mensional Kadomstev-Petviashvili equation for describing the fractal water wave in this work. The non-differentiable transform is utilized to convert the local frac?tional equation into a local fractional ODE. On defining the Mittag-Leffler function on the Cantor sets, then a trial function based on the Mittag-Leffler function is proposed to seek for the non-differentiable exact solutions. The results reveal that the proposed method is a promising way to study the local fractional PDE arising in engineering and physics.