Abstract
Based on the local fractional derivative, we develop a new local fractional (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. With the help of the traveling wave transform of the nondifferentiable type, we convert the local fractional equation into a nonlinear local fractional ordinary differential equation (ODE). Then the Mittag-Leffler function-based method is presented here for the first time to construct the abundant nondifferentiable exact traveling wave solutions, and three families (six sets) of the exact solutions are obtained. In addition, the performances of different solutions on the Cantor set are presented via numerical results in the form of 3D plots. It reveals that the proposed method is simple and straightforward, which can be used to study the local fractional partial differential equations (PDEs).
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