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 ${\mathrm{\text{LT}}}_{\delta }({\mathrm{\Xi }}^{\delta })$ and ${\mathrm{\text{LC}}}_{\delta }({\mathrm{\Xi }}^{\delta })$ 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 $\delta =ln2/ln3$ are depicted graphically. Additionally, as a comparison, the ESs of the classic (3+1)-dimensional MZKe for $\delta =1$ 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.

分数阶导数在许多领域得到了广泛的应用并引起了广泛的关注。本文首次用局部分数阶导数（LFD）提取了一个新的分数（3+1）维修正扎哈罗夫-库兹涅佐夫方程（MZKe）。两个特殊的函数，即${\mathrm{\text{LT}}}_{\delta }（{\mathrm{\Xi }}^{\delta }）$和${\mathrm{\text{液相色谱}}}_{\delta }（{\mathrm{\Xi }}^{\delta }）$基于康托集 (CS) 上定义的 Mittag-Leffler 函数 (MLF) 导出的函数用于构造辅助试验函数以研究精确解 (ES)。在 Yang 的不可微 (ND) 变换的帮助下，发现了六组 ND ES。CS 上的 ND ES 用于$\delta =因2/因3$均以图形方式描绘。此外，作为比较，经典 (3+1) 维 MZKe 的 ES$\delta =1$也有图解说明。结果表明，推导的方法强大且有效，可用于处理其他局部分数偏微分方程。