Title

Discrete fractional calculus with the nabla operator

Author(s)

Ferhan M. Atici, Western Kentucky University
Paul W. Eloe, University of DaytonFollow

Document Type

Article

Publication Date

2009

Publication Source

Electronic Journal of Qualitative Theory of Differential Equations

Abstract

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.

Inclusive pages

No. 3, 12

ISBN/ISSN

1417-3875

Document Version

Published Version

Comments

Honoring the career of John Graef on the occasion of his sixty-seventh birthday

This document is made available in compliance with the publisher's policy on self-archiving or with the express permission of the publisher. Permission documentation is on file.

Volume

Special Edition I

Peer Reviewed

yes

eCommons Citation

Atici, Ferhan M. and Eloe, Paul W., "Discrete fractional calculus with the nabla operator" (2009). Mathematics Faculty Publications. 105.
https://ecommons.udayton.edu/mth_fac_pub/105