Superdiffusion is usually described by an equation with a Riesz-type fractional spatial derivative. The derivative is nonlocal in space, so it is difficult to impose boundary conditions for this equation at a partially permeable thin membrane. If we define the function g appropriately, then the g-subdiffusion equation with the Caputo time derivative with respect to another function g also describes superdiffusion. The Green`s functions for both equations mentioned above converge in the long-time limit. The advantages of using the g-subdiffusion equation to describe superdiffusion will be presented, in particular, the ability to define boundary conditions at the membrane. The presentation is based on the following publications: T. Kosztolowicz, Phys. Rev. E 107, 064103 (2023), 106, L022104 (2022), 99, 022127 (2019), and T. Kosztolowicz, A.Dutkiewicz, Phys. Rev. E 104, 014118 (2021), 104 L042101 (2021).