The two types of calculus within quantum calculus are q-calculus and h-calculus.
Notes on verification
Multiple independent academic sources including the authoritative textbook by Kac and Cheung (Springer) explicitly confirm q-calculus and h-calculus as the two fundamental types of quantum calculus. Corroboration from peer-reviewed papers in Project Euclid and arXiv strengthens this verification. While extensions exist, the core categorization is well-established in mathematical literature.
Sources
- Quantum calculus (en.wikipedia.org)
- https://link.springer.com/chapter/10.1007/978-1-4613-0071-7_1 (link.springer.com)
- https://books.google.de/books/about/Quantum_Calculus.html?hl=ru&id=mK8HXHSTbB0C&redir_esc=y (books.google.de)
- https://link.springer.com/book/10.1007/978-1-4613-0071-7 (link.springer.com)
- https://www.amazon.com/Quantum-Calculus-Universitext-Victor-Kac/dp/0387953418 (amazon.com)
- https://projecteuclid.org/journals/tbilisi-mathematical-journal/volume-10/issue-2/The-presentation-of-a-new-type-of-quantum-calculus/10.1515/tmj-2017-0022.pdf (projecteuclid.org)
- https://arxiv.org/pdf/1911.10623 (arxiv.org)
- https://arxiv.org/pdf/1008.0672 (arxiv.org)