Generalized Variational Structure of the Fractal Modified Kdv–zakharov–kuznetsov Equation

A fractal modification of the modified KdV–Zakharov–Kuznetsov equation is suggested and its fractal generalized variational structure is established by means of the semi-inverse method. Furthermore, the obtained fractal generalized variational structure is discussed and verified through the two-scale transform from another dimension field in detail. The obtained fractal generalized variational structure reveals the conservation laws via the energy form in the fractal space and can be employed to study the fractal solitary wave properties.