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Analytical and numerical convexity results for discrete fractional sequential differences with negative lower bound.
- Source :
-
Journal of Difference Equations & Applications . Mar2021, Vol. 27 Issue 3, p317-341. 25p. - Publication Year :
- 2021
-
Abstract
- We investigate relationships between the sign of the discrete fractional sequential difference ( Δ 1 + a − μ ν Δ a μ f) (t) and the convexity of the function t ↦ f (t). In particular, we consider the case in which the bound ( Δ 1 + a − μ ν Δ a μ f) (t) ≥ ε f (a) , for some ε > 0 and where f (a) < 0 , is satisfied. Thus, we allow for the case in which the sequential difference may be negative, and we show that even though the fractional difference can be negative, the convexity of the function f can be implied by the above inequality nonetheless. This demonstrates a significant dissimilarity between the fractional and non-fractional cases. We use a combination of both hard analysis and numerical simulation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 27
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 150019755
- Full Text :
- https://doi.org/10.1080/10236198.2021.1894142