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title:
 
Fractional q-Calculus on a time scale
publication:
 
JNMP
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
publication date:
 
October 2007
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:
 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/by-nc/4.0/
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