title: |
Fractional q-Calculus on a time scale |
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publication: |
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| volume-issue: | 14 - 3 | |
| pages: | 341 - 352 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2007.14.3.4 (how to use a DOI) | |
author(s): |
Ferhan M. Atici, Paul W. Eloe |
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publication date: |
October 2007 |
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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.
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copyright: |
©
Atlantis Press. This is an open-access article distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |