> That sounds like a hoax to me. I had to look up fractional calculus, but it appears to be a real thing. It still sounds ridiculous and appears to bring in memcapitive and meminductive elements to their odd new world.

Fractional calculus is a well established tool to develop physical models, particularly rheological and damping models. It makes sense to apply the same technique to model circuit components as rheological and electronic models do share quite a bit of common ground, and in some cases even symbolic representation.