EXACT TRAVELING WAVE SOLUTIONS TO THE LOCAL FRACTIONAL (3 + 1)-DIMENSIONAL JIMBO–MIWA EQUATION ON CANTOR SETS

Abstract

In this work, we derive a new fractional [Formula: see text]-dimensional Jimbo–Miwa equation via the local fractional derivative. With the help of the traveling wave transform of the non-differentiable type, the local fractional [Formula: see text]-dimensional Jimbo–Miwa equation is converted into a nonlinear local fractional ordinary differential equation. Then, a new method named as Mittag-Leffler function-based method is used to construct the exact traveling wave solutions for the first time. Four families (eight sets) of the traveling wave solutions are obtained and the behaviors of the solutions on Cantor sets are presented via the 3D plot. The results show that the proposed method is a powerful tool to study the traveling wave theory of the local fractional equations.