Some relations between the Caputo fractional difference operators and integer-order differences

In this article, we are concerned with the relationships between the sign of Caputo fractional differences and integer nabla differences. In particular, we show that if $N-1<\nu<N$, $f:\mathbb{N}_{a-N+1}\to\mathbb{R}$, $\nabla^\nu_{a^*}f(t)\geq 0$, for $t\in\mathbb{N}_{a+1}$ and $\nabla^{N-1}f...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2015; no. 163; pp. 1 - 7
Main Authors Baoguo Jia, Lynn Erbe, Allan Peterson
Format Journal Article
LanguageEnglish
Published Texas State University 17.06.2015
Subjects
Caputo fractional difference
monotonicity
Taylor monomial
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Summary:In this article, we are concerned with the relationships between the sign of Caputo fractional differences and integer nabla differences. In particular, we show that if $N-1<\nu<N$, $f:\mathbb{N}_{a-N+1}\to\mathbb{R}$, $\nabla^\nu_{a^*}f(t)\geq 0$, for $t\in\mathbb{N}_{a+1}$ and $\nabla^{N-1}f(a)\geq 0$, then $\nabla^{N-1}f(t)\geq 0$ for $t\in\mathbb{N}_a$.
ISSN:1072-6691