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A new fractal Rosenau–Burgers equation with He’s fractal derivative is proposed in this work. Exerting the semi-inverse method, two different kinds of the generalized fractal variational principles (GFVPs) of the fractal Rosenau–Burgers equation are constructed. The GFVPs extracted in this paper are expected to bring some new inspiration for the study and application of the variational method in the fractal space.
Xu et al. (2024) studied this question.