Non-classical analysis

In mathematics, non-classical analysis is any system of analysis, other than classical real analysis, and complex, vector, tensor, etc., analysis based upon it.

Such systems include:

Non-standard analysis and the calculus it involves, non-standard calculus, are considered part of classical mathematics (i.e. The concept of "hyperreal number" it uses, can be constructed in the framework of Zermelo-Fraenkel set theory).

...
Wikipedia