Volume 17, Issue 1, March 2010, Pages 51 - 68
On (q, h)-Analogue of Fractional Calculus
Received 13 February 2009, Accepted 7 September 2009, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925110000593How to use a DOI?
- Keywords
- Fractional integral; fractional derivative; (q, h)-calculus; time scale; generalized Gamma function
- Abstract
The paper discusses fractional integrals and derivatives appearing in the so-called (q, h)-calculus which is reduced for h = 0 to quantum calculus and for q = h = 1 to difference calculus. We introduce delta as well as nabla version of these notions and present their basic properties. Furthermore, we give comparisons with the known results and discuss possible extensions to more general settings.
- Copyright
- © 2010 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Jan Čermák AU - Luděk Nechvátal PY - 2021 DA - 2021/01/07 TI - On (q, h)-Analogue of Fractional Calculus JO - Journal of Nonlinear Mathematical Physics SP - 51 EP - 68 VL - 17 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925110000593 DO - 10.1142/S1402925110000593 ID - Čermák2021 ER -