Non-Differentiable Exact Solutions of the Local Fractional Zakharov–kuznetsov Equation on the Cantor Sets

In this study, a new fractional Zakharov–Kuznetsov equation (ZKE) within the local fractional derivative (LFD) is derived. Yang’s non-differentiable (ND) traveling wave transform is introduced, then two novel techniques namely the Mittag-Leffler function-based method (MLFBM) and Yang’s special function method (Y-SFM) are adopted to seek for the ND exact solutions for the first time. With the aid of the Mathematica software, the dynamic behaviors of the different solutions on the Cantor sets are illustrated via the 3D plots by assigning the appropriate parameters. The attained results confirm that the mentioned methods are effective and straightforward, which can be used to study the ND exact solutions of the local fractional partial differential equations (PDEs).