Effect of <i>Fangzhu's</i> nanoscale surface morphology on water collection

Abstract

This paper suggests a fractal mathematical model for Fangzhu 's water collection by taking into account its nanoscale surface morphology. A fractal variational principle is established by the semi‐inverse method, which elucidates the conservation laws in the fractal space. Additionally, the variational formulation can also reveal the structure of the solution. An approximate analytical solution is obtained via the two‐scale transform method and He's frequency formula. Some special cases of the model are discussed numerically, showing the method is remarkably simple and capable to solve nonlinear oscillators with fractal derivatives.

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