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Zbl 1189.39004
Atici, F.M.; Eloe, P.
Discrete fractional calculus with the nabla operator. (English)
[J] Electron. J. Qual. Theory Differ. Equ. 2009, Spec. Iss. I, Paper No. 3, 12 p., electronic only (2009). ISSN 1417-3875/e

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.

MSC 2000:: *39A12 Discrete version of topics in analysis
26A33 Fractional derivatives and integrals (real functions)
44A10 Laplace transform

Keywords: discrete fractional calculus; exponential laws; product rule; Laplace transform; time scale; fractional finite difference equation; gamma function

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