<?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%">D.B. DHAIGUDE</style></author><author><style face="normal" font="default" size="100%">SANDEEP P. BHAIRAT</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND UNIQUENESS OF SOLUTION OF CAUCHY-TYPE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">CAUCHY-TYPE PROBLEM FOR HILFER FRACTIONAL EQUATIONS</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">26A33</style></keyword><keyword><style  face="normal" font="default" size="100%">34A08</style></keyword><keyword><style  face="normal" font="default" size="100%">34A12</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%">01/2018</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/22/1/8.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">22</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><isbn><style face="normal" font="default" size="100%">1083-2564</style></isbn><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;The Cauchy-type problem for a nonlinear differential equation involving Hilfer (generalized Riemann-Liouville) fractional derivative is&amp;nbsp;considered. The equivalence between this Cauchy-type problem and a nonlinear Volterra integral equation in the space of weighted continuous functions&amp;nbsp;is established. Using this result, existence, uniqueness and continuous dependence of solution for Cauchy-type problem are obtained by using successive&amp;nbsp;approximations and the generalized Gronwall inequality.&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%">121</style></section></record></records></xml>