<?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%">T. ABDELJAWAD</style></author><author><style face="normal" font="default" size="100%">D. BALEANULO</style></author><author><style face="normal" font="default" size="100%">F. JARAD</style></author><author><style face="normal" font="default" size="100%">O. G. MUSTAFA</style></author><author><style face="normal" font="default" size="100%">J. J. TRUJILLO</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A FITE TYPE RESULT FOR SEQUENTIAL FRACTIONAL DIFFERENTIAL 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%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34C10</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%">2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/19/27-DSA-29-12.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%">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;Given the solution f of the sequential fractional differential equation&lt;/p&gt;

&lt;p&gt;&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t&lt;/sub&gt; (&amp;nbsp;&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t&lt;/sub&gt; f ) + P( t ) f = 0, t ∈ [b, c],&amp;nbsp; &amp;nbsp; where&amp;nbsp; &amp;nbsp;−∞ &amp;lt; a &amp;lt; b &amp;lt; c &amp;lt; +∞, α ∈ (1/ 2 , 1)&amp;nbsp; &amp;nbsp; and&amp;nbsp; &amp;nbsp;P : [a, +∞) → [ 0, P&lt;sub&gt;∞&lt;/sub&gt;], P&lt;sub&gt;∞&lt;/sub&gt; &amp;lt; +∞,&amp;nbsp; &amp;nbsp; is continuous. Assume that there exist&amp;nbsp; &amp;nbsp;t&lt;sub&gt;1&lt;/sub&gt;, t&lt;sub&gt;2&lt;/sub&gt; ∈ [b, c]&amp;nbsp; such that&amp;nbsp; f( t&lt;sub&gt;1&amp;nbsp;&lt;/sub&gt;) = (&lt;sub&gt;a&lt;/sub&gt;D&lt;sup&gt;α&lt;/sup&gt;&lt;sub&gt;t &lt;/sub&gt;f )( t&lt;sub&gt;2&amp;nbsp;&lt;/sub&gt;) = 0. Then, we establish here a positive lower bound for c − a which depends solely on α, P&lt;sub&gt;∞&lt;/sub&gt;. Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations.&lt;/p&gt;
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