In this paper, we introduce two new generalized core inverses, namely, the (p,q,m)-core inverse and ⟨p,q,n⟩-core inverse; both extend inverses of ⟨i,m⟩-core inverse, (j,m)-core core-EP DMP-inverse.

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...