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^...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2015-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/163/abstr.html |
| _version_ | 1811256454197280768 |
|---|---|
| author | Baoguo Jia Lynn Erbe Allan Peterson |
| author_facet | Baoguo Jia Lynn Erbe Allan Peterson |
| author_sort | Baoguo Jia |
| collection | DOAJ |
| description | 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 $t\in\mathbb{N}_a$. |
| first_indexed | 2024-04-12T17:40:18Z |
| format | Article |
| id | doaj.art-4b26909097b84fc4ae29901775c0b06c |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T17:40:18Z |
| publishDate | 2015-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-4b26909097b84fc4ae29901775c0b06c2022-12-22T03:22:49ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-06-012015163,17Some relations between the Caputo fractional difference operators and integer-order differencesBaoguo Jia0Lynn Erbe1Allan Peterson2 Sun Yat-Sen Univ., Guangzhou, China Univ. of Nebraska, Lincoln, NE, USA Univ. of Nebraska, Lincoln, NE, USA 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 $t\in\mathbb{N}_a$.http://ejde.math.txstate.edu/Volumes/2015/163/abstr.htmlCaputo fractional differencemonotonicityTaylor monomial |
| spellingShingle | Baoguo Jia Lynn Erbe Allan Peterson Some relations between the Caputo fractional difference operators and integer-order differences Electronic Journal of Differential Equations Caputo fractional difference monotonicity Taylor monomial |
| title | Some relations between the Caputo fractional difference operators and integer-order differences |
| title_full | Some relations between the Caputo fractional difference operators and integer-order differences |
| title_fullStr | Some relations between the Caputo fractional difference operators and integer-order differences |
| title_full_unstemmed | Some relations between the Caputo fractional difference operators and integer-order differences |
| title_short | Some relations between the Caputo fractional difference operators and integer-order differences |
| title_sort | some relations between the caputo fractional difference operators and integer order differences |
| topic | Caputo fractional difference monotonicity Taylor monomial |
| url | http://ejde.math.txstate.edu/Volumes/2015/163/abstr.html |
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