<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">RAZIYE MERT</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author><author><style face="normal" font="default" size="100%">THABET ABDELJAWAD</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIQUENESS OF SOLUTIONS OF NABLA FRACTIONAL DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">asymptotic property</style></keyword><keyword><style  face="normal" font="default" size="100%">contraction mapping theorem</style></keyword><keyword><style  face="normal" font="default" size="100%">existence and uniqueness</style></keyword><keyword><style  face="normal" font="default" size="100%">nabla fractional difference equation</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2019</style></year><pub-dates><date><style  face="normal" font="default" size="100%">02/2019</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/28/1/11.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">28</style></volume><pages><style face="normal" font="default" size="100%">12</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem&amp;nbsp;to be incomplete. By using Contraction Mapping Theorem, we establish conditions&amp;nbsp;under which solutions exist and are unique and have certain asymptotic properties.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">183</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">XIANG LIU</style></author><author><style face="normal" font="default" size="100%">BAOGUO JIA</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">STABILITY RESULTS FOR NONLINEAR FRACTIONAL ORDER h-DIFFERENCE SYSTEMS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A70</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">07/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/27/3/10.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">20</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;This paper is concerned with the stability of the fractional order&amp;nbsp;h-difference systems. The definition of Mittag-Leffler stability is introduced, and the&amp;nbsp;sufficient conditions are presented by extending the Lyapunov direct method to such&amp;nbsp;systems. Moreover, we weaken the restriction on Lyapunov function, the stability of&amp;nbsp;the fractional order h-difference systems is established. Two numerical examples are&amp;nbsp;given to illustrate our main results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">609</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">JIA BAOGUO</style></author><author><style face="normal" font="default" size="100%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">ALLAN PETERSON</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">MONOTONICITY AND CONVEXITY FOR NABLA FRACTIONAL q-DIFFERENCES</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications </style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">26A48</style></keyword><keyword><style  face="normal" font="default" size="100%">39A70</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99.</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://www.acadsol.eu/dsa/articles/25/4.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">25</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;In this paper, we examine the relation between monotonicity and convexity for nabla fractional q-differences. In particular we prove that&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Theorem A. &lt;/strong&gt;Assume $f : q^{N_0} \longrightarrow R$, $\nabla^{\nu}_q f(t) ≥ 0$ for each $t \in&amp;nbsp;q^{N_0}$, with $1 &amp;lt; \nu&amp;nbsp;&amp;lt; 2$, then $\nabla_q f(t) \geq&amp;nbsp;0$ for $t\in q^{N_1}$.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Theorem B.&lt;/strong&gt; Assume $f : q^{N_0} \longrightarrow R$, $\nabla^{\nu}_q f(t) ≥ 0$ for each $t \in&amp;nbsp;q^{N_1}$, with $2&amp;nbsp;&amp;lt; \nu&amp;nbsp;&amp;lt; 3$, then $\nabla_q^2 f(t) \geq&amp;nbsp;0$ for $t\in q^{N_2}$.&lt;/p&gt;

&lt;p&gt;This shows that, in some sense, the positivity of the $\mu$-th order $q$-fractional difference has a strong connection to the monotonicity and convexity of $f(t)$.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%"> 47</style></section></record></records></xml>