Journal
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
Volume 14, Issue 3, Pages 333-344Publisher
SPRINGERNATURE
DOI: 10.2991/jnmp.2007.14.3.4
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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 T-t0 = {t : t = t(0)q(n), n a nonnegative integer} boolean OR {0}, where t(0) is an element of 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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