Atici, F. M.; Eloe, P. Discrete fractional calculus with the nabla operator. (English) Zbl 1189.39004 Electron. J. Qual. Theory Differ. Equ. 2009, Spec. Iss. I, Paper No. 3, 12 p. (2009). Summary: Properties of discrete fractional calculus in the sense of a backward difference are introduced and developed. Exponential laws and a product rule are developed and relations to the forward fractional calculus are explored. Properties of the Laplace transform for the nabla derivative on the time scale of integers are developed and a fractional finite difference equation is solved with a transform method. As a corollary, two new identities for the gamma function are exhibited. Cited in 1 ReviewCited in 204 Documents MSC: 39A12 Discrete version of topics in analysis 26A33 Fractional derivatives and integrals 44A10 Laplace transform Keywords:discrete fractional calculus; exponential laws; product rule; Laplace transform; time scale; fractional finite difference equation; gamma function PDFBibTeX XMLCite \textit{F. M. Atici} and \textit{P. Eloe}, Electron. J. Qual. Theory Differ. Equ. 2009, Paper No. 3, 12 p. (2009; Zbl 1189.39004) Full Text: DOI EuDML EMIS