Discrete fractional calculus with the nabla operator

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 sca...

Full description

Saved in:
Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2009; no. 3; pp. 1 - 12
Main Authors Atici, Ferhan M., Eloe, Paul
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2009
Online AccessGet full text

Cover

More Information
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.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2009.4.3