Volume 14, Issue 3, October 2007, Pages 341 - 352
Fractional q-Calculus on a time scale
Authors
Ferhan M. Atici, Paul W. Eloe
Corresponding Author
Ferhan M. Atici
Received 2 June 2006, Accepted 8 January 2007, Available Online 1 October 2007.
- DOI
- 10.2991/jnmp.2007.14.3.4How to use a DOI?
- Abstract
The study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus on a time scale Tt0 = {t : t = t0 q n , n a nonnegative integer } ∪ {0}, where t0 ∈ R and 0 < q < 1. By use of time scale calculus notation, we find the proof of many results more straight forward. We shall develop some properties of fractional q-calculus, we shall develop some properties of a q-Laplace transform, and then we shall employ the q-Laplace transform to solve fractional q-difference equations.
- Copyright
- © 2007, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Ferhan M. Atici AU - Paul W. Eloe PY - 2007 DA - 2007/10/01 TI - Fractional q-Calculus on a time scale JO - Journal of Nonlinear Mathematical Physics SP - 341 EP - 352 VL - 14 IS - 3 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2007.14.3.4 DO - 10.2991/jnmp.2007.14.3.4 ID - Atici2007 ER -