{"id":2490,"date":"2021-01-11T20:17:57","date_gmt":"2021-01-11T20:17:57","guid":{"rendered":"https:\/\/dynamicpublishers.org\/?page_id=2490"},"modified":"2021-01-31T15:09:51","modified_gmt":"2021-01-31T15:09:51","slug":"10-discrete-version-of-gronwall-bellman-type-inequality-and-its-application-in-stability-analysis","status":"publish","type":"page","link":"https:\/\/dynamicpublishers.org\/?page_id=2490","title":{"rendered":"#10 &#8211; Discrete Version of Gronwall-Bellman Type Inequality and Its Application in Stability Analysis"},"content":{"rendered":"\n<p><strong>Rabia Ilyas Butt, Thabet Abdeljawad, <\/strong>and <strong>Mujeeb Ur Rehman <\/strong>&nbsp;. Discrete Version of Gronwall-Bellman Type Inequality and Its Application in Stability Analysis. Dynamic Systems and Applications 30 (2021) No.3,&nbsp; 449-459<\/p>\n\n\n\n<p><a href=\"https:\/\/doi.org\/10.46719\/dsa202130310\">https:\/\/doi.org\/10.46719\/dsa202130310<\/a><\/p>\n\n\n\n<p><strong>ABSTRACT. <\/strong><br>In this article, we develop a new discrete version of Gronwall-Bellman type inequality. Then, using the newly developed&nbsp; inequality to discuss Ulam-Hyers stability of a Caputo nabla fractional difference system. An example is provided to illustrate the theoretical results. Our analysis is applied on an isolated&nbsp; time scale equivalent&nbsp; to $h\\mathbb{Z}$.<\/p>\n\n\n\n<p><strong>AMS (MOS) Subject Classification<\/strong>. 39A30.<\/p>\n\n\n\n<p><strong>Key Words.<\/strong> Gronwall-Bellman inequality, Caputo nabla fractional difference system, Existence, Uniqueness, Ulam-Hyers stability<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/dynamicpublishers.org\/?page_id=614\" target=\"_blank\" rel=\"noreferrer noopener\">Purchase Article<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link\" href=\"https:\/\/dynamicpublishers.org\/wp-content\/uploads\/2021\/01\/30-A28-Butt.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Download<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Rabia Ilyas Butt, Thabet Abdeljawad, and Mujeeb Ur Rehman &nbsp;. Discrete Version of Gronwall-Bellman Type Inequality and Its Application in Stability Analysis. Dynamic Systems and Applications 30 (2021) No.3,&nbsp; 449-459 https:\/\/doi.org\/10.46719\/dsa202130310 ABSTRACT. In this article, we develop a new discrete version of Gronwall-Bellman type inequality. Then, using the newly developed&nbsp; inequality to discuss Ulam-Hyers stability [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-2490","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/pages\/2490","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2490"}],"version-history":[{"count":2,"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/pages\/2490\/revisions"}],"predecessor-version":[{"id":2543,"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=\/wp\/v2\/pages\/2490\/revisions\/2543"}],"wp:attachment":[{"href":"https:\/\/dynamicpublishers.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}