Variational principles for two kinds of non-linear geophysical KdV equation with fractal derivatives

It is an important and difficult inverse problem to construct variational principles from complex models directly, because their formulations are theoretical bases for many methods solve or analyze the non-linear problems. At first, this paper extends two kinds of geophysical KdV equations in continuum mechanics fractional partners fractal porous media with irregular boundaries. Then, by designing skillfully, trial-Lagrange functional, successfully established equation Coriolis term, high-order extended derivatives, respectively. Furthermore, obtained proved be correct minimizing functionals calculus variations.