Initial value problems in discrete fractional calculus
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- by Ferhan M. Atici and Paul W. Eloe
- Proc. Amer. Math. Soc. 137 (2009), 981-989
- DOI: https://doi.org/10.1090/S0002-9939-08-09626-3
- Published electronically: September 10, 2008
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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.References
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Bibliographic 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
- MR Author ID: 63110
- ORCID: 0000-0002-6590-9931
- Email: Paul.Eloe@notes.udayton.edu
- Received by editor(s): February 25, 2008
- Published electronically: September 10, 2008
- Communicated by: Jane M. Hawkins
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 981-989
- MSC (2000): Primary 39A12, 34A25, 26A33
- DOI: https://doi.org/10.1090/S0002-9939-08-09626-3
- MathSciNet review: 2457438