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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Initial value problems in discrete fractional calculus


Authors: Ferhan M. Atici and Paul W. Eloe
Journal: Proc. Amer. Math. Soc. 137 (2009), 981-989
MSC (2000): Primary 39A12, 34A25, 26A33
Published electronically: September 10, 2008
MathSciNet review: 2457438
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Abstract: This paper is devoted to the study of discrete fractional calculus; the particular goal is to define and solve well-defined discrete fractional difference equations. For this purpose we first carefully develop the commutativity properties of the fractional sum and the fractional difference operators. Then a $ \nu$-th ( $ 0 < \nu \leq 1$) order fractional difference equation is defined. A nonlinear problem with an initial condition is solved and the corresponding linear problem with constant coefficients is solved as an example. Further, the half-order linear problem with constant coefficients is solved with a method of undetermined coefficients and with a transform method.


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Additional Information

Ferhan M. Atici
Affiliation: Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky 42101-3576
Email: ferhan.atici@wku.edu

Paul W. Eloe
Affiliation: Department of Mathematics, University of Dayton, Dayton, Ohio 45469-2316
Email: Paul.Eloe@notes.udayton.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09626-3
PII: S 0002-9939(08)09626-3
Keywords: Discrete fractional calculus
Received by editor(s): February 25, 2008
Published electronically: September 10, 2008
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.