Abstract
In this paper, we investigate the local fractional Kundu–Mukherjee–Naskar (LFKMN) equation in (2+1) dimensional case. The Yang’s local fractional calculus tool has fulfilled a significant character in defining the fractal behaviours in a fractal space or microgravity space that arise in applied nonlinear sciences. The travelling wave transformation of the non-differentiable type is introduced and we retrieve successfully the non-differentiable exact traveling wave solutions (soliton pulses in (2+1)-dimensions) of LFKMN equation with aid of generalized exp-function method in the form of generalized functions described on Cantor sets. With the help of Mathematica package program, 3D graphs were drawn for the special values of the parameters in the solutions, and the physical structures of the solutions obtained in this way were also observed. The solutions obtained can be used in the explanation of physical phenomena occurring in propagation of rogue waves in oceans and higher order optical solitons in optical fibers in current-like nonlinearities.The deduced explicit solutions will cause a new pathway of the nonlinear wave theory by the help of local fractional derivative. The proposed approach is demostrated to ensure a beneficial tool to solve the local fractional nonlinear evolution equations in applied nonlinear sciences.