<?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%">A.K. TRIPATHY</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NEW OSCILLATION CRITERIA FOR FOURTH ORDER NEUTRAL DYNAMIC EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><alt-title><style face="normal" font="default" size="100%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">FOURTH ORDER NEUTRAL DYNAMIC EQUATIONS</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A10</style></keyword><keyword><style  face="normal" font="default" size="100%">34K11</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%">01/2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/20/1/2.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</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&gt;In this paper, the oscillation of a class of fourth order nonlinear neutral functional dynamic equations of the form&lt;/p&gt;

&lt;p&gt;$$ \left(r(t)  (y(t) + p(t)y(\alpha(t)))^{\Delta^2}\right)^{\Delta^2} + q(t)f(y(\beta(t))) = 0 $$&lt;/p&gt;

&lt;p&gt;is studied on an arbitrary time scale $T$, under the assumption&lt;br /&gt;
$$&lt;br /&gt;
\int\limits_{t_0}^{\infty} \frac{t}{r(t)} \Delta&amp;nbsp;t = \infty, \quad t_0 &amp;gt; 0,&lt;br /&gt;
$$&lt;br /&gt;
for various ranges of $p(t)$.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">13</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%">JAGAN MOHAN JONNALAGADDA</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">PERIODIC SOLUTIONS OF FRACTIONAL NABLA DIFFERENCE EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><alt-title><style face="normal" font="default" size="100%">CAA</style></alt-title><short-title><style face="normal" font="default" size="100%">Fractional Nabla Difference Equations</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">39A23</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%">11/2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/20/4/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">26</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 article, we discuss periodic properties of nonlinear fractional nabla difference systems. First, we prove that any given system of fractional nabla difference equations doesn’t possess a nonconstant periodic solution. Next, we establish sufficient conditions on existence and uniqueness of S-asymptotically periodic solutions for the same. Finally, we provide few examples to illustrate the applicability of established results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">4</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">585</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%">LYNN ERBE</style></author><author><style face="normal" font="default" size="100%">TAHER S. HASSAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">COMPARISON THEOREMS FOR HIGHER ORDER FORCED NONLINEAR FUNCTIONAL DYNAMIC EQUATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/1/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">16</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;The purpose of this paper is to establish comparison criteria for higher order forced nonlinear dynamic equation with mixed nonlinearities $${ \left\{&amp;nbsp; r_{n−1}(t) (r_{n−2}(t)(· · ·(r_1(t)x^∆(t))^∆ · · ·)^∆)^∆&amp;nbsp; \right\}^∆ + \sum_{j=0}^{N} &amp;nbsp;p_j (t) ϕ_{γ_j} ( x (\varphi_j (t)) &amp;nbsp;= g(t) , }$$ on an above-unbounded time scale${ \mathbb{T} }$, where ${ n ≥ 2}$. The results improve the main results of a number of recent papers and are established for a time scale ${ \mathbb{T} }$ without assuming certain restrictive conditions on ${ \mathbb{T} }$.&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">79</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%">RAVI P. AGARWAL</style></author><author><style face="normal" font="default" size="100%">SAID R. GRACE</style></author><author><style face="normal" font="default" size="100%">TAHER S. HASSAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION CRITERIA FOR HIGHER ORDER NONLINEAR FUNCTIONAL DYNAMIC EQUATIONS WITH MIXED NONLINEARITIES</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/3/5.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">33</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we will consider the higher-order functional dynamic equations with mixed nonlinearities of the form $${ \left\{&amp;nbsp;&amp;nbsp;r_{n−1}(t) \phi_{αn−1} [ (r_{n−2}(t)(· · ·(r_1(t)\phi_{α1} [x^∆(t)])^∆ · · ·)^∆)^∆] \right.\} ^∆ + \sum^{N}_{ j=0} p_j (t)\phi_{γj} (x^σ (g_j (t))) = 0, }$$ on an above-unbounded time scale ${ \mathbb{T} }$, where ${ n ≥ 2 }$, and ${ \phi_β(u) := |u|^{β−1} \&amp;nbsp; u, β &amp;gt; 0. }$&amp;nbsp; The funtions ${ g_j : \mathbb{T} → \mathbb{T} }$ are rd-continuous functions such that ${ lim_{t→∞} g_j (t) = ∞, \&amp;nbsp; j = 0, 1, . . . , N. }$ The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><section><style face="normal" font="default" size="100%">369</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%">RAEGAN HIGGINS</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">OSCILLATION OF CERTAIN DYNAMIC EQUATIONS ON TIME SCALES</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">34K11</style></keyword><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/19/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">15</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;Oscillation criteria are established for second-order nonlinear nabla dynamic equations on an isolated time scale ${ \mathbb{T} }$. Our main goal is to establish a relationship between the oscillatory behavior of these equations. We also give two results about the behavior of a second-order self-adjoint equation with mixed derivatives on a time scale that is unbounded above. We use the Riccati transformation technique to obtain our results.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><section><style face="normal" font="default" size="100%">113</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%">J. VASUNDHARA DEVI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXTREMAL SOLUTIONS AND CONTINUOUS DEPENDENCE FOR SET DIFFERENTIAL EQUATIONS INVOLVING CAUSAL OPERATORS WITH MEMORY</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">SET DIFFERENTIAL EQUATIONS INVOLVING CAUSAL OPERATORS</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">01/2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/1/9.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">124</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;div class=&quot;rtejustify&quot;&gt;In this paper we proceed to present results pertaining to extremal solutions and continuous dependence of solutions with respect to initial values and a parameter for set differential equations involving causal operators with memory.&lt;/div&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">113</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%">G. V. S. R. DEEKSHITULU</style></author><author><style face="normal" font="default" size="100%">J. JAGAN MOHAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">FRACTIONAL DIFFERENCE INEQUALITIES OF BIHARI TYPE</style></title><secondary-title><style face="normal" font="default" size="100%">Communications in Applied Analysis</style></secondary-title><short-title><style face="normal" font="default" size="100%">FRACTIONAL DIFFERENCE INEQUALITIES OF BIHARI TYPE</style></short-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">39A10</style></keyword><keyword><style  face="normal" font="default" size="100%">39A99</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">08/2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/14/3/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">14</style></volume><pages><style face="normal" font="default" size="100%">354</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, using the properties of ∇&lt;sup&gt;−α&lt;/sup&gt; , some discrete fractional inequalities of Bihari-type are established.&lt;/p&gt;
</style></abstract><issue><style face="normal" font="default" size="100%">3</style></issue><work-type><style face="normal" font="default" size="100%">scientific: mathematics</style></work-type><section><style face="normal" font="default" size="100%">343</style></section></record></records></xml>