Abstract
In this study, we present the idea of variational fractal transform method to find the analytical solution for the fractal Kawahara equation that arises in shallow water waves in the microgravity space or with the unsmooth boundary. The fractal semi-inverse method is used to establish a fractal variational formulation of the problem, which provides the analysis of the soliton solution and its physical properties. An example is considered to show that this new scheme is straightforward and efficient, and can be generalized to other nonlinear evolution equations with fractal derivatives performance.
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