I cite (on the adjacent page linked at the top) doi:10.1016/j.jmaa.2007.03.081 which sites them. But, as far as I know, all that stuff is doing regular formal limits-based calculus.

I haven't yet come-across the notion of these non-Newtonian infinitesimals in particular.

Thanks for the link to that page though, it is a good starting point for seeing what other things may be going on!

Thanks again, that link is really good!

I think the bi in bigeometic refers to how the domain and range are both made greometric? That corresponds to elasticity, but not the multiplicative derivation and integral in my examples. That (which is exactly the concepts from the paper I cited above) would be called by them the geometric calculus (mono, no bi) I think.

(I since did a larger edit which makes good use of that :).)