<?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%">MOHAMED ABDALLA DARWISH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">NONDECREASING SOLUTIONS OF A FRACTIONAL QUADRATIC INTEGRAL EQUATION OF URYSOHN-VOLTERRA TYPE</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%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">45M99</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</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%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/28-DSA-1175.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%">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;In this paper we study a very general quadratic integral equation of fractional order. We show that the quadratic integral equations of fractional orders has at least one monotonic solution in the Banach space of all real functions defined and continuous on a bounded and closed interval. The concept of a measure of noncompactness related to monotonicity, introduced by J. Bana´s and L. Olszowy, and a fixed point theorem due to Darbo are the main tools in carrying out our proof. In fact we generalize, improve the results of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005), 112–119]. Also, we extend and generalize the results of the paper [J. Bana´s and B. Rzepka, Monotonic solutions of a quadratic integral equation of fractional order, J. Math. Anal. Appl. 332 (2007), 1370–1378].&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">423</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%">MOHAMED DARWISH</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">ON MONOTONIC SOLUTIONS OF A SINGULAR QUADRATIC INTEGRAL EQUATION WITH SUPREMUM</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%">45G10</style></keyword><keyword><style  face="normal" font="default" size="100%">45M99</style></keyword><keyword><style  face="normal" font="default" size="100%">47H09</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-539-550.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">11</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;We prove an existence theorem for a singular quadratic integral equation with supremum. The quadratic integral equation studied below contains as a special case numerous integral equations encountered in the theory of radiative transfer and in the kinetic theory of gases. We show that the singular quadratic integral equations with supremum has a monotonic solution in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.&lt;/p&gt;
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