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

Saved in:
Bibliographic Details
Published in:Electronic journal of differential equations 2015-06, Vol.2015 (163), p.1-7
Main Authors: Baoguo Jia, Lynn Erbe, Allan Peterson
Format: Article
Language:English
Subjects:
Caputo fractional difference
monotonicity
Taylor monomial
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page 7
container_issue 163
container_start_page 1
container_title Electronic journal of differential equations
container_volume 2015
creator Baoguo Jia
Lynn Erbe
Allan Peterson
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
format article
fullrecord <record><control><sourceid>doaj</sourceid><recordid>TN_cdi_doaj_primary_oai_doaj_org_article_4b26909097b84fc4ae29901775c0b06c</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><doaj_id>oai_doaj_org_article_4b26909097b84fc4ae29901775c0b06c</doaj_id><sourcerecordid>oai_doaj_org_article_4b26909097b84fc4ae29901775c0b06c</sourcerecordid><originalsourceid>FETCH-LOGICAL-d221t-b1ea142d43002c7f9dda380d1311e7ce4d65f216216961e66889bf181dc11e8b3</originalsourceid><addsrcrecordid>eNpNjN1KAzEUhPdCwVp9h7zAQk42zW4uZfGnUPDCeh1OkpOast2UJCK-vevPhczAwMzHXDQr4L1oldJw1VyXcuQctBRy1ZiXdCKWacIa01yYpfpBNLP6RmzE83tNLGR03yNOzMcQKNPsiKUzZawpF4azZ3GudKDcpuwp_8PKTXMZcCp0-5fr5vXhfj8-tbvnx-14t2u9EFBbC4QghZcd58L1QXuP3cA9dADUO5JebYIAtVgrIKWGQdsAA3i3AIPt1s3299cnPJpzjifMnyZhND9FygeDuUY3kZFWKM0X9XaQwUkkoTWHvt84brly3RdNvVyq</addsrcrecordid><sourcetype>Open Website</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Some relations between the Caputo fractional difference operators and integer-order differences</title><source>DOAJ Directory of Open Access Journals</source><creator>Baoguo Jia ; Lynn Erbe ; Allan Peterson</creator><creatorcontrib>Baoguo Jia ; Lynn Erbe ; Allan Peterson</creatorcontrib><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 $N-1&lt;\nu&lt;N$, $f:\mathbb{N}_{a-N+1}\to\mathbb{R}$, $\nabla^\nu_{a^*}f(t)\geq 0$, for $t\in\mathbb{N}_{a+1}$ and $\nabla^{N-1}f(a)\geq 0$, then $\nabla^{N-1}f(t)\geq 0$ for $t\in\mathbb{N}_a$.</description><identifier>ISSN: 1072-6691</identifier><language>eng</language><publisher>Texas State University</publisher><subject>Caputo fractional difference ; monotonicity ; Taylor monomial</subject><ispartof>Electronic journal of differential equations, 2015-06, Vol.2015 (163), p.1-7</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,2096</link.rule.ids></links><search><creatorcontrib>Baoguo Jia</creatorcontrib><creatorcontrib>Lynn Erbe</creatorcontrib><creatorcontrib>Allan Peterson</creatorcontrib><title>Some relations between the Caputo fractional difference operators and integer-order differences</title><title>Electronic journal of differential equations</title><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 $N-1&lt;\nu&lt;N$, $f:\mathbb{N}_{a-N+1}\to\mathbb{R}$, $\nabla^\nu_{a^*}f(t)\geq 0$, for $t\in\mathbb{N}_{a+1}$ and $\nabla^{N-1}f(a)\geq 0$, then $\nabla^{N-1}f(t)\geq 0$ for $t\in\mathbb{N}_a$.</description><subject>Caputo fractional difference</subject><subject>monotonicity</subject><subject>Taylor monomial</subject><issn>1072-6691</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>DOA</sourceid><recordid>eNpNjN1KAzEUhPdCwVp9h7zAQk42zW4uZfGnUPDCeh1OkpOast2UJCK-vevPhczAwMzHXDQr4L1oldJw1VyXcuQctBRy1ZiXdCKWacIa01yYpfpBNLP6RmzE83tNLGR03yNOzMcQKNPsiKUzZawpF4azZ3GudKDcpuwp_8PKTXMZcCp0-5fr5vXhfj8-tbvnx-14t2u9EFBbC4QghZcd58L1QXuP3cA9dADUO5JebYIAtVgrIKWGQdsAA3i3AIPt1s3299cnPJpzjifMnyZhND9FygeDuUY3kZFWKM0X9XaQwUkkoTWHvt84brly3RdNvVyq</recordid><startdate>20150617</startdate><enddate>20150617</enddate><creator>Baoguo Jia</creator><creator>Lynn Erbe</creator><creator>Allan Peterson</creator><general>Texas State University</general><scope>DOA</scope></search><sort><creationdate>20150617</creationdate><title>Some relations between the Caputo fractional difference operators and integer-order differences</title><author>Baoguo Jia ; Lynn Erbe ; Allan Peterson</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-d221t-b1ea142d43002c7f9dda380d1311e7ce4d65f216216961e66889bf181dc11e8b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Caputo fractional difference</topic><topic>monotonicity</topic><topic>Taylor monomial</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Baoguo Jia</creatorcontrib><creatorcontrib>Lynn Erbe</creatorcontrib><creatorcontrib>Allan Peterson</creatorcontrib><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Electronic journal of differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Baoguo Jia</au><au>Lynn Erbe</au><au>Allan Peterson</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Some relations between the Caputo fractional difference operators and integer-order differences</atitle><jtitle>Electronic journal of differential equations</jtitle><date>2015-06-17</date><risdate>2015</risdate><volume>2015</volume><issue>163</issue><spage>1</spage><epage>7</epage><pages>1-7</pages><issn>1072-6691</issn><abstract>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 $N-1&lt;\nu&lt;N$, $f:\mathbb{N}_{a-N+1}\to\mathbb{R}$, $\nabla^\nu_{a^*}f(t)\geq 0$, for $t\in\mathbb{N}_{a+1}$ and $\nabla^{N-1}f(a)\geq 0$, then $\nabla^{N-1}f(t)\geq 0$ for $t\in\mathbb{N}_a$.</abstract><pub>Texas State University</pub><tpages>7</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1072-6691
ispartof Electronic journal of differential equations, 2015-06, Vol.2015 (163), p.1-7
issn 1072-6691
language eng
recordid cdi_doaj_primary_oai_doaj_org_article_4b26909097b84fc4ae29901775c0b06c
source DOAJ Directory of Open Access Journals
subjects Caputo fractional difference
monotonicity
Taylor monomial
title Some relations between the Caputo fractional difference operators and integer-order differences
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T16%3A41%3A46IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-doaj&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Some%20relations%20between%20the%20Caputo%20fractional%20difference%20operators%20and%20integer-order%20differences&rft.jtitle=Electronic%20journal%20of%20differential%20equations&rft.au=Baoguo%20Jia&rft.date=2015-06-17&rft.volume=2015&rft.issue=163&rft.spage=1&rft.epage=7&rft.pages=1-7&rft.issn=1072-6691&rft_id=info:doi/&rft_dat=%3Cdoaj%3Eoai_doaj_org_article_4b26909097b84fc4ae29901775c0b06c%3C/doaj%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-d221t-b1ea142d43002c7f9dda380d1311e7ce4d65f216216961e66889bf181dc11e8b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true