Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations
In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theo...
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| Veröffentlicht in: | Qualitative theory of dynamical systems 2023-06, Vol.22 (2), Article 81 |
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| container_title | Qualitative theory of dynamical systems |
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| creator | Shahid, Sumbel Saifullah, Shahid Riaz, Usman Zada, Akbar Moussa, Sana Ben |
| description | In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theorems, respectively. Uniqueness and at least one solution of corresponding coupled form of the proposed nonlinear system will be prove through Banach contraction theorem and Arzel
a
`
–Ascoli theorem, respectively. Under some hypothesis, we scrutinize Hyers–Ulam stability of the mentioned nonlinear equation and its corresponding coupled nonlinear system. For the support of our main results, we present examples. |
| doi_str_mv | 10.1007/s12346-023-00772-5 |
| format | Article |
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a
`
–Ascoli theorem, respectively. Under some hypothesis, we scrutinize Hyers–Ulam stability of the mentioned nonlinear equation and its corresponding coupled nonlinear system. For the support of our main results, we present examples.</description><identifier>ISSN: 1575-5460</identifier><identifier>EISSN: 1662-3592</identifier><identifier>DOI: 10.1007/s12346-023-00772-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Difference and Functional Equations ; Differential equations ; Dynamical Systems and Ergodic Theory ; Fixed points (mathematics) ; Mathematics ; Mathematics and Statistics ; Nonlinear equations ; Nonlinear systems ; Stability ; Theorems ; Uniqueness theorems</subject><ispartof>Qualitative theory of dynamical systems, 2023-06, Vol.22 (2), Article 81</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-c87e10b24e0709d96f994df21743e38a5b3816aa0f60522299f65992971eb5703</citedby><cites>FETCH-LOGICAL-c319t-c87e10b24e0709d96f994df21743e38a5b3816aa0f60522299f65992971eb5703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12346-023-00772-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12346-023-00772-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Shahid, Sumbel</creatorcontrib><creatorcontrib>Saifullah, Shahid</creatorcontrib><creatorcontrib>Riaz, Usman</creatorcontrib><creatorcontrib>Zada, Akbar</creatorcontrib><creatorcontrib>Moussa, Sana Ben</creatorcontrib><title>Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations</title><title>Qualitative theory of dynamical systems</title><addtitle>Qual. Theory Dyn. Syst</addtitle><description>In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theorems, respectively. Uniqueness and at least one solution of corresponding coupled form of the proposed nonlinear system will be prove through Banach contraction theorem and Arzel
a
`
–Ascoli theorem, respectively. Under some hypothesis, we scrutinize Hyers–Ulam stability of the mentioned nonlinear equation and its corresponding coupled nonlinear system. For the support of our main results, we present examples.</description><subject>Difference and Functional Equations</subject><subject>Differential equations</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Fixed points (mathematics)</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear equations</subject><subject>Nonlinear systems</subject><subject>Stability</subject><subject>Theorems</subject><subject>Uniqueness theorems</subject><issn>1575-5460</issn><issn>1662-3592</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKt_wFXAdTSPSdIspbZaKApV1yEzTUrKdNImGbD_3tQR3Lm6r-8cLgeAW4LvCcbyIRHKKoEwZaiMkiJ-BkZECIoYV_S89FxyxCuBL8FVSluMBZWMjsBm9uVTtl1joenW8D2b2rc-H-HKpr7NCboQ4WvoWt9ZE-Fit2994zNcFTrs4DyaJvvQmRYuumw3MaAn75yNtsu-LGeH3pzu6RpcONMme_Nbx-BzPvuYvqDl2_Ni-rhEDSMqo2YiLcE1rSyWWK2VcEpVa0eJrJhlE8NrNiHCGOwE5pRSpZzgSlElia25xGwM7gbffQyH3qast6GP5b-kqVSywFyoQtGBamJIKVqn99HvTDxqgvUpUD0Eqkug-idQzYuIDaJU4G5j45_1P6pvPkB4ug</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>Shahid, Sumbel</creator><creator>Saifullah, Shahid</creator><creator>Riaz, Usman</creator><creator>Zada, Akbar</creator><creator>Moussa, Sana Ben</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations</title><author>Shahid, Sumbel ; Saifullah, Shahid ; Riaz, Usman ; Zada, Akbar ; Moussa, Sana Ben</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-c87e10b24e0709d96f994df21743e38a5b3816aa0f60522299f65992971eb5703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Difference and Functional Equations</topic><topic>Differential equations</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Fixed points (mathematics)</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear equations</topic><topic>Nonlinear systems</topic><topic>Stability</topic><topic>Theorems</topic><topic>Uniqueness theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shahid, Sumbel</creatorcontrib><creatorcontrib>Saifullah, Shahid</creatorcontrib><creatorcontrib>Riaz, Usman</creatorcontrib><creatorcontrib>Zada, Akbar</creatorcontrib><creatorcontrib>Moussa, Sana Ben</creatorcontrib><collection>CrossRef</collection><jtitle>Qualitative theory of dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shahid, Sumbel</au><au>Saifullah, Shahid</au><au>Riaz, Usman</au><au>Zada, Akbar</au><au>Moussa, Sana Ben</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations</atitle><jtitle>Qualitative theory of dynamical systems</jtitle><stitle>Qual. Theory Dyn. Syst</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>22</volume><issue>2</issue><artnum>81</artnum><issn>1575-5460</issn><eissn>1662-3592</eissn><abstract>In this typescript, we present nonlinear implicit random fractional integro-differential equation in mean square sense and its corresponding coupled system. For the existence, uniqueness and at least one solution of the said nonlinear equation, we use Banach contraction and Schauder fixed point theorems, respectively. Uniqueness and at least one solution of corresponding coupled form of the proposed nonlinear system will be prove through Banach contraction theorem and Arzel
a
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| subjects | Difference and Functional Equations Differential equations Dynamical Systems and Ergodic Theory Fixed points (mathematics) Mathematics Mathematics and Statistics Nonlinear equations Nonlinear systems Stability Theorems Uniqueness theorems |
| title | Existence and Stability Results for Nonlinear Implicit Random Fractional Integro-Differential Equations |
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