A NOVEL COMPUTATIONAL APPROACH TO THE LOCAL FRACTIONAL (3+1)-DIMENSIONAL MODIFIED ZAKHAROV–KUZNETSOV EQUATION

Abstract

The fractional derivatives have been widely applied in many fields and has attracted widespread attention. This paper extracts a new fractional (3+1)-dimensional modified Zakharov–Kuznetsov equation (MZKe) with the local fractional derivative (LFD) for the first time. Two special functions, namely, the [Formula: see text] and [Formula: see text] functions that are derived on the basis of the Mittag-Leffler function (MLF) defined on the Cantor set (CS), are employed to construct the auxiliary trial function to look into the exact solutions (ESs). Aided by Yang’s non-differentiable (ND) transformation, six groups of the ND ESs are found. The ND ESs on the CS for [Formula: see text] are depicted graphically. Additionally, as a comparison, the ESs of the classic (3+1)-dimensional MZKe for [Formula: see text] are also illustrated. The outcomes reveal that the derived method is powerful and effective, and can be used to deal with the other local fractional PDEs.