Existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delays

Li, Shuang; Shu, Linxin; Shu, Xu; Xu, Fei

doi:10.1080/17442508.2018.1551400

Cited by 66 publications

(34 citation statements)

References 30 publications

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“…Definition 2.4 (see [19]) Equation (1.1) is Hyers-Ulam stable if, for any ε > 0, there exists a solution y(t) which satisfies the above inequality and has the same initial value as…”

Section: Definition 23mentioning

confidence: 99%

The existence and Hyers–Ulam stability of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1 < β < 2 $1<\beta<2$

Guo

Shu

et al. 2019

Bound Value Probl

Self Cite

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This paper deals with the existence of solution for an impulsive Riemann-Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1 < β < 2 and its Hyers-Ulam stability. We prove the mild solutions for the equation using basic theorems of fractional differential equation. The existence result of the equation is obtained by Mönch's fixed point theorem. Finally, we prove the Hyers-Ulam stability of the solution.

show abstract

“…Definition 2.4 (see [19]) Equation (1.1) is Hyers-Ulam stable if, for any ε > 0, there exists a solution y(t) which satisfies the above inequality and has the same initial value as…”

Section: Definition 23mentioning

confidence: 99%

The existence and Hyers–Ulam stability of solution for an impulsive Riemann–Liouville fractional neutral functional stochastic differential equation with infinite delay of order 1 < β < 2 $1<\beta<2$

Guo

Shu

et al. 2019

Bound Value Probl

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the literature, there are a few papers about the HUS and the HURS of stochastic systems (see [13,[27][28][29][30]). The stability of SFDEs has attracted much more attention (see [2,19] etc.).…”

Section: Introductionmentioning

confidence: 99%

Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

Makhlouf

Mchiri

Rhaima

2021

Journal of Function Spaces

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The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.

show abstract

“…e result of the work of Alsina and Ger was extended to the Hyers-Ulam stability of a higher-order differential equation with constant coefficients in [6]. We mention here only the recent contributions in this subject of some mathematicians [6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Fourier Transformation and Stability of a Differential Equation on $L^{1} (Rezaei 1, Zafarasa 2, Karimi 3 2021 International Journal of Mathematics and Mathematical Sciences2000View full text Add to dashboard CiteIn the present paper, by the Fourier transform, we show that every linear differential equation with constant coefficients of

n

-th order has a solution in

L

1

ℝ

which is infinitely differentiable in

ℝ
∖

0

. Moreover the Hyers–Ulam stability of such equations on

L

1

ℝ

is investigated.show abstractscite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health. Contact Info hi@scite.ai 10624 S. Eastern Ave., Ste. 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Made with 💙 for researchers Part of the Research Solutions Family.window.__SCITE_STORE_STATE = {"addReportDashboardModal":{"selectedPapers":[]},"ui":{"referralPartner":null,"freeReports":0,"bannerContent":null,"bannerClosed":false,"navMenu":{},"createDashboardFromSearchResultsModalShow":false,"savedSearchModalShow":false,"searchFilterModalShow":false,"flagModalShow":false,"resetPasswordModalShow":false,"loginModalShow":false,"referenceCheckModalShow":false,"deleteDashboardModalShow":false,"addReportToDashboardModalShow":false,"shareDashboardModalShow":false,"editDashboardModalShow":false,"upgradeModalShow":false,"exportReportModalShow":false,"exportReferenceModalShow":false,"generateCitationModalShow":false,"exportDashboardModalShow":false,"dashboardLimitErrorModalShow":false,"whatIsThisReportModalShow":false,"whatIsThisSearchModalShow":false,"whatIsAssistantModalShow":false,"trialOverModalShow":false,"activateTrialModalShow":false,"cancelTrialCheckoutModalShow":false,"cookieModalShow":false,"personaModalShow":false,"modalFromContext":"","shownModals":[],"hasUser":false,"user":null,"ipLocationData":{"data":null,"error":false,"loading":false},"fetchingUser":false,"savingUser":false,"saveUserError":false,"onboardingLoadTracker":{"state":undefined},"userEntitlements":null,"entitlementsLoading":false,"referralsLoading":false,"pageError":null,"browser":null,"extensionLoaded":false,"organizationLicense":{"hasLicense":false},"linkResolver":null,"sickoMode":false,"authors":[],"navOpen":false,"showMobileSearch":false,"redeemCodeLoading":false,"redeemCodeError":null,"redeemCodeSuccess":false,"applyDiscountLoading":false,"applyDiscountError":null,"applyDiscountSuccess":false,"userDiscount":null,"search":{"term":"","focused":false,"autocompletesLoadTracker":{},"autocompletes":{}},"referencesToExport":[],"citeGeneratorPaperData":{},"dimensions":{},"cookiePreference":null,"userChurnKey":null,"churnKeyLoading":false,"fullTextLinkState":{},"agAvailabilityState":{}},"verifyEmail":{"loading":false,"verified":false,"expired":false},"dashboard":{"id":"","name":"","displayName":"","normalizedName":"","description":"","slug":"","dashboardType":"","accessType":"","isPublic":null,"componentLayout":[],"doiQuery":{},"journalMetadata":{},"affiliationMetadata":{},"institutionMetadata":{},"haveAccessToDashboard":null,"lastUpdated":null,"doisUpdatedTS":null,"doisRefreshedTS":null,"refreshStatus":"","loadState":{},"deleteDashboardError":false,"deletingDashboard":false,"totalDoiCount":0,"matchedDoiCount":0,"unmatchedDoiCount":0,"exportLoadTracker":{},"setDashboardUsersLoading":false,"setDashboardUsersError":false,"setDashboardUsersSuccess":false,"dashboardAccessList":null,"getDashboardAccessListLoading":false,"getDashboardAccessListSuccess":false,"getDashboardAccessListError":false},"notifications":{"notifications":[],"loading":false,"error":null,"notificationItems":[],"notificationItemsLoading":false,"notificationItemsError":null,"notificationItemsPage":1,"notificationItemsTotal":0,"newNotificationItems":0,"notificationItemsFilters":{},"dropDownNotificationItems":[],"dropDownNotificationItemsLoading":false,"dropDownNotificationItemsError":null,"notificationSetStatusLoading":false,"notificationSetStatusError":null},"report":{"paper":"10.1080\u002F17442508.2018.1551400","tally":"10.1080\u002F17442508.2018.1551400","citations":[{"id":2010840741,"source":"10.1186\u002Fs13661-019-1172-6","target":"10.1080\u002F17442508.2018.1551400","negative":0.015449766442179678,"positive":0.01747467927634716,"neutral":1,"section":"definition 23","type":"mentioning","typeConfidence":1,"snippet":"Definition 2.4 (see \u003Ccite data-doi=\"10.1080\u002F17442508.2018.1551400\"\u003E[19]\u003C\u002Fcite\u003E) Equation (1.1) is Hyers-Ulam stable if, for any ε > 0, there exists a solution y(t) which satisfies the above inequality and has the same initial value as","lang":"en","langConfidence":"0.8999999761581421","refLocation":"b18\u002F1","memberId":297,"selfCites":[{"type":"SHAREDAUTHOR","family":"Shu","given":"Xiao-Bao"},{"type":"SHAREDAUTHOR","family":"Xu","given":"Fei"}],"snippetHidden":false},{"id":2446053542,"source":"10.1155\u002F2021\u002F5544847","target":"10.1080\u002F17442508.2018.1551400","negative":0.004318512137979269,"positive":0.005499233957380056,"neutral":1,"section":"introduction","type":"mentioning","typeConfidence":1,"snippet":"In the literature, there are a few papers about the HUS and the HURS of stochastic systems (see \u003Ccite data-doi=\"10.1080\u002F07362994.2020.1824677\"\u003E[13,\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1016\u002Fj.spl.2020.108949\"\u003E[27]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1080\u002F17442508.2018.1551400\"\u003E[28]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.7153\u002Fdea-09-15\"\u003E[29]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1186\u002Fs13662-016-1002-4\"\u003E[30]\u003C\u002Fcite\u003E). The stability of SFDEs has attracted much more attention (see \u003Ccite data-doi=\"10.1533\u002F9780857099402.47\"\u003E[2,\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1016\u002Fj.spl.2015.07.033\"\u003E19]\u003C\u002Fcite\u003E etc.).","lang":"en","langConfidence":"0.949999988079071","refLocation":"b27\u002F1","memberId":98,"selfCites":[],"snippetHidden":false},{"id":2510644575,"source":"10.1155\u002F2021\u002F5524430","target":"10.1080\u002F17442508.2018.1551400","negative":0.003325833287090063,"positive":0.007893289439380169,"neutral":1,"section":"introduction","type":"mentioning","typeConfidence":1,"snippet":"e result of the work of Alsina and Ger was extended to the Hyers-Ulam stability of a higher-order differential equation with constant coefficients in \u003Ccite data-doi=\"10.1016\u002Fj.jmaa.2003.12.044\"\u003E[6]\u003C\u002Fcite\u003E. We mention here only the recent contributions in this subject of some mathematicians \u003Ccite data-doi=\"10.1016\u002Fj.jmaa.2003.12.044\"\u003E[6]\u003C\u002Fcite\u003E[7]\u003Ccite data-doi=\"10.1080\u002F07362994.2020.1824677\"\u003E[8]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1155\u002F2009\u002F576852\"\u003E[9]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1080\u002F17442508.2018.1551400\"\u003E[10]\u003C\u002Fcite\u003E[11][12][13][14]\u003Ccite data-doi=\"10.1016\u002Fj.aml.2007.10.020\"\u003E[15]\u003C\u002Fcite\u003E.","lang":"en","langConfidence":"0.8799999952316284","refLocation":"b9\u002F1","memberId":98,"selfCites":[],"snippetHidden":false},{"id":2517739951,"source":"10.1155\u002F2021\u002F5539306","target":"10.1080\u002F17442508.2018.1551400","negative":0.00236316192895174,"positive":0.0030111197847872972,"neutral":1,"section":"introduction","type":"mentioning","typeConfidence":1,"snippet":"Evolution equations interpret the differential law of development with respect to time. A vast theory, in this regard, has been developed [1][2]\u003Ccite data-doi=\"10.1112\u002Fblms\u002F19.3.288\"\u003E[3]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1080\u002F07362994.2020.1824677\"\u003E[4]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1080\u002F17442508.2018.1551400\"\u003E[5]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1016\u002F0362-546x(81)90047-x\"\u003E[6]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1007\u002F978-3-319-66384-5\"\u003E[7]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.3934\u002Fcpaa.2020084\"\u003E[8]\u003C\u002Fcite\u003E\u003Ccite data-doi=\"10.1016\u002Fj.jmaa.2020.124288\"\u003E[9]\u003C\u002Fcite\u003E. In \u003Ccite data-doi=\"10.1090\u002Fs0002-9939-2012-11613-2\"\u003E[10]\u003C\u002Fcite\u003E, Hernándaz and O'Regan established the theory of noninstantaneous impulsive equations and showed the existence of corresponding mild solutions.","lang":"en","langConfidence":"0.8600000143051147","refLocation":"b4\u002F1","memberId":98,"selfCites":[],"snippetHidden":false},{"id":2445957504,"source":"10.1155\u002F2020\u002F9372406","target":"10.1080\u002F17442508.2018.1551400","negative":0.005814397148787975,"positive":0.040059540420770645,"neutral":1,"section":"introduction","type":"mentioning","typeConfidence":1,"snippet":"Many mathematicians had considered the wide scope of this same problem for fractional equations of different types. 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We prove the mild solutions for the equation using basic theorems of fractional differential equation. The existence result of the equation is obtained by Mönch's fixed point theorem. Finally, we prove the Hyers-Ulam stability of the solution.","authors":[{"family":"Guo","given":"Yuchen","affiliation":"Hunan University","authorSlug":"yuchen-guo-N11kP","authorName":"Yuchen Guo","authorID":"1046727","authorLastKnownAffiliationId":10824,"authorSequenceNumber":1,"affiliationSlug":"hunan-university-EjMy","affiliationID":"17461"},{"family":"Shu","given":"Xu","affiliation":"Hunan University","authorSlug":"xu-shu-W8wD55","authorName":"Xu Shu","authorID":"7197192","authorLastKnownAffiliationId":198670,"authorSequenceNumber":2,"affiliationSlug":"hunan-university-EjMy","affiliationID":"17461"},{"family":"Li","given":"Yongjin","affiliation":"Sun Yat-sen University","authorSlug":"yongjin-li-zRd0M8","authorName":"Yongjin Li","authorID":"4909250","authorLastKnownAffiliationId":1029,"authorSequenceNumber":3,"affiliationSlug":"sun-yat-sen-university-LDla","affiliationID":"4240"},{"family":"Xu","given":"Fei","affiliation":"Wilfrid Laurier University","authorSlug":"fei-xu-8G0y99","authorName":"Fei Xu","authorID":"6692121","authorLastKnownAffiliationId":4231,"authorSequenceNumber":4,"affiliationSlug":"wilfrid-laurier-university-Yb4P","affiliationID":"25795"}],"keywords":["Impulsive Riemann-Liouville fractional differential equation","Stochastic differential equation","Mönch's fixed point theorem","Hausdorff measure of noncompactness","Hyers-Ulam stability"],"year":2019,"shortJournal":"Bound Value Probl","publisher":"Springer Science and Business Media LLC","issue":"1","volume":"2019","retracted":false,"memberId":297,"issns":["1687-2770"],"editorialNotices":[],"journalSlug":"boundary-value-problems-OVap4","journal":"Boundary Value Problems","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1155\u002F2020\u002F9372406":{"id":9776755470,"doi":"10.1155\u002F2020\u002F9372406","slug":"existence-and-hyers-ulam-stability-of-RVaYv0KN","type":"journal-article","title":"Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters","abstract":"This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.","authors":[{"family":"Luo","given":"Danfeng","affiliation":"Guizhou University","authorSlug":"danfeng-luo-ejxnGK","authorName":"Danfeng Luo","authorID":"6484111","authorLastKnownAffiliationId":2002,"authorSequenceNumber":1,"affiliationSlug":"guizhou-university-9OOk","affiliationID":"2002"},{"family":"Luo","given":"Zhiguo","affiliation":"Hunan Normal University","authorSlug":"zhiguo-luo-5GWXlR","authorName":"Zhiguo Luo","authorID":"6958869","authorLastKnownAffiliationId":14267,"authorSequenceNumber":2,"affiliationSlug":"hunan-normal-university-Jn2G","affiliationID":"14267"},{"family":"Qiu","given":"Hongjun","affiliation":"Jiujiang University","authorSlug":"hongjun-qiu-KW0Rye","authorName":"Hongjun Qiu","authorID":"10806679","authorLastKnownAffiliationId":3054,"authorSequenceNumber":3,"affiliationSlug":"jiujiang-university-zZDE","affiliationID":"18806"}],"keywords":[],"year":2020,"shortJournal":"Mathematical Problems in Engineering","publisher":"Hindawi Limited","volume":"2020","page":"1-12","memberId":98,"issns":["1563-5147","1024-123X"],"editorialNotices":[],"journalSlug":"mathematical-problems-in-engineering-0G2v9","journal":"Mathematical Problems in Engineering","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1155\u002F2021\u002F5544847":{"id":11002475680,"doi":"10.1155\u002F2021\u002F5544847","slug":"ulam-hyers-rassias-stability-of-stochastic-functional-lZKAlL4b","type":"journal-article","title":"Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods","abstract":"The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.","authors":[{"family":"Makhlouf","given":"Abdellatif Ben","affiliation":"Al Jouf University","authorSlug":"abdellatif-ben-makhlouf-KWPb5l","authorName":"Abdellatif Ben Makhlouf","authorID":"8055479","authorLastKnownAffiliationId":377,"authorSequenceNumber":1,"affiliationSlug":"al-jouf-university-zdV8","affiliationID":"25206"},{"family":"Mchiri","given":"Lassaad","affiliation":"King Saud University","authorSlug":"lassaad-mchiri-gX4QpK","authorName":"Lassaad Mchiri","authorID":"14772714","authorLastKnownAffiliationId":161514,"authorSequenceNumber":2,"affiliationSlug":"king-saud-university-3NxW","affiliationID":"10900"},{"family":"Rhaima","given":"Mohamed","affiliation":"King Saud University","authorSlug":"mohamed-rhaima-xQE4gW","authorName":"Mohamed Rhaima","authorID":"10217422","authorLastKnownAffiliationId":10900,"authorSequenceNumber":3,"affiliationSlug":"king-saud-university-3NxW","affiliationID":"10900"}],"year":2021,"shortJournal":"Journal of Function Spaces","publisher":"Hindawi Limited","volume":"2021","page":"1-7","memberId":98,"issns":["2314-8888","2314-8896"],"editorialNotices":[],"journalSlug":"journal-of-function-spaces-EWmL1","journal":"Journal of Function Spaces","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1155\u002F2021\u002F5524430":{"id":11137326652,"doi":"10.1155\u002F2021\u002F5524430","slug":"fourier-transformation-and-stability-of-MVbbWGm9","type":"journal-article","title":"Fourier Transformation and Stability of a Differential Equation on \u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" id=\"M1\"\u003E\n \u003Cmsup\u003E\n \u003Cmrow\u003E\n \u003Cmi\u003EL\u003C\u002Fmi\u003E\n \u003C\u002Fmrow\u003E\n \u003Cmrow\u003E\n \u003Cmn\u003E1\u003C\u002Fmn\u003E\n \u003C\u002Fmrow\u003E\n \u003C\u002Fmsup\u003E\n \u003Cmfenced open=\"(\" close=\")\" separators=\"|\"\u003E\n \u003Cmrow\u003E\n \u003Cmi\u003E","abstract":"In the present paper, by the Fourier transform, we show that every linear differential equation with constant coefficients of \n \n n\n \n -th order has a solution in \n \n \n \n L\n \n \n 1\n \n \n \n \n ℝ\n \n \n \n which is infinitely differentiable in \n \n ℝ\n ∖\n \n \n 0\n \n \n \n . Moreover the Hyers–Ulam stability of such equations on \n \n \n \n L\n \n \n 1\n \n \n \n \n ℝ\n \n \n \n is investigated.","authors":[{"family":"Rezaei","given":"Hamid","affiliation":"Yasouj University","authorSlug":"hamid-rezaei-9OPYOb","authorName":"Hamid Rezaei","authorID":"7316190","authorLastKnownAffiliationId":214220,"authorSequenceNumber":1,"affiliationSlug":"yasouj-university-pL9Y","affiliationID":"18630"},{"family":"Zafarasa","given":"Zahra","affiliation":"Yasouj University","authorSlug":"zahra-zafarasa-5GpyN2","authorName":"Zahra Zafarasa","authorID":"6302669","authorLastKnownAffiliationId":18630,"authorSequenceNumber":2,"affiliationSlug":"yasouj-university-pL9Y","affiliationID":"18630"},{"family":"Karimi","given":"Lotfollah","affiliation":"Hamedan University of Technology","authorSlug":"lotfollah-karimi-6MxXJg","authorName":"Lotfollah Karimi","authorID":"11240598","authorLastKnownAffiliationId":136511,"authorSequenceNumber":3,"affiliationSlug":"hamedan-university-of-technology-ej8Rm","affiliationID":"136511"}],"keywords":[],"year":2021,"shortJournal":"International Journal of Mathematics and Mathematical Sciences","publisher":"Hindawi Limited","volume":"2021","page":"1-7","memberId":98,"issns":["1687-0425","0161-1712"],"editorialNotices":[],"journalSlug":"international-journal-of-mathematics-and-J1zKY","journal":"International Journal of Mathematics and Mathematical Sciences","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1155\u002F2021\u002F5539306":{"id":11143302564,"doi":"10.1155\u002F2021\u002F5539306","slug":"existence-theorem-for-noninstantaneous-impulsive-y8X0ZjJM","type":"journal-article","title":"Existence Theorem for Noninstantaneous Impulsive Evolution Equations","abstract":"In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.","authors":[{"family":"Aslam","given":"Gul I Hina","affiliation":"National University of Sciences and Technology","authorSlug":"gul-i-hina-aslam-rZ2v5A","authorName":"Gul I Hina Aslam","authorID":"23547373","authorLastKnownAffiliationId":2138,"authorSequenceNumber":1,"affiliationSlug":"national-university-of-sciences-and-V0yz","affiliationID":"2138"},{"family":"Ali","given":"Amjad","affiliation":"University of Debrecen","authorSlug":"amjad-ali-A36jyZ","authorName":"Amjad Ali","authorID":"7351705","authorLastKnownAffiliationId":16683,"authorSequenceNumber":2,"affiliationSlug":"university-of-debrecen-Ljlm","affiliationID":"13940"},{"family":"Rafiq","given":"M.","affiliation":"COMSATS University Islamabad","authorSlug":"m-rafiq-zRJ24b","authorName":"M. 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For example, external forces can abruptly change the model; impulses and delay can cause a breakdown of it. Considering these intrinsic phenomena in the mathematical model makes the difference between a simple differential equation and a differential equation with impulses, delay, and nonlocal conditions. So, in this work, we consider a semilinear nonautonomous neutral differential equation under the influence of impulses, delay, and nonlocal conditions. In this paper we study the controllability of these semilinear neutral differential equations with some of these intrinsic phenomena taking into consideration. Our aim is to prove that the controllability of the associated ordinary linear differential equation is preserved under certain conditions imposed on these new disturbances. In order to achieve our objective, we apply Rothe's fixed point Theorem to prove the exact controllability of the system. Finally, our method can be extended to the evolution equation in Hilbert spaces with applications to control systems governed by PDE's equations.","authors":[{"family":"Camacho","given":"Oscar","affiliation":"Universidad San Francisco de Quito","authorSlug":"oscar-camacho-68ANEM","authorName":"Oscar Camacho","authorID":"6931498","authorLastKnownAffiliationId":17578,"authorSequenceNumber":1,"affiliationSlug":"universidad-san-francisco-de-quito-OgM8","affiliationID":"17578"},{"family":"Leiva","given":"Hugo","affiliation":"Universidad Yachay Tech","authorSlug":"hugo-leiva-wbmZkM","authorName":"Hugo Leiva","authorID":"7588228","authorLastKnownAffiliationId":174722,"authorSequenceNumber":2,"affiliationSlug":"universidad-yachay-tech-bQA1","affiliationID":"20259"},{"family":"Riera-Segura","given":"Lenin","affiliation":"Universidad Yachay Tech","authorSlug":"lenin-riera-segura-8668NO","authorName":"Lenin Riera-Segura","authorID":"26848721","authorLastKnownAffiliationId":20259,"authorSequenceNumber":3,"affiliationSlug":"universidad-yachay-tech-bQA1","affiliationID":"20259"}],"keywords":["controllability of neutral equations","semilinear equations","impulses","nonlocal conditions","rothe's fixed point theorem"],"year":2022,"shortJournal":"Math Methods in App Sciences","publisher":"Wiley","issue":"16","volume":"45","page":"9826-9839","memberId":311,"issns":["0170-4214","1099-1476"],"editorialNotices":[],"journalSlug":"mathematical-methods-in-the-applied-y808a","journal":"Mathematical Methods in the Applied Sciences","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1002\u002Fmma.9163":{"id":11631659824,"doi":"10.1002\u002Fmma.9163","slug":"ulam-type-stability-for-caputo-hadamard-kePpGgRy","type":"journal-article","title":"Ulam type stability for Caputo–Hadamard fractional functional stochastic differential equations with delay","abstract":"This paper addresses the existence of stability results for Ulam–Hyers (UHS) and Ulam–Hyers–Rassias (UHRS) in the setting of Caputo–Hadamard fractional functional stochastic differential equations with delay (FFSDEwD). We first prove existence and uniqueness using Banach fixed point theorem coupled with standard stochastic analysis techniques. Then, we deal with UHS and UHRS results of Caputo–Hadamard FFSDEwD through an application of Gronwall inequality. Our theoretical findings are corroborated with two numerical examples.","authors":[{"family":"Rhaima","given":"Mohamed","affiliation":"King Saud University","authorSlug":"mohamed-rhaima-xQE4gW","authorName":"Mohamed Rhaima","authorID":"10217422","authorLastKnownAffiliationId":10900,"authorSequenceNumber":1,"affiliationSlug":"king-saud-university-3NxW","affiliationID":"10900"}],"keywords":["Banach space","Caputo–Hadamard derivative","fractional stochastic differential equations","Mittag–Leffler function","Ulam–Hyers–Rassias stability"],"year":2023,"shortJournal":"Math Methods in App Sciences","publisher":"Wiley","issue":"9","volume":"46","page":"10995-11006","memberId":311,"issns":["0170-4214","1099-1476"],"editorialNotices":[],"journalSlug":"mathematical-methods-in-the-applied-y808a","journal":"Mathematical Methods in the Applied Sciences","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1002\u002Fmma.9287":{"id":11644236176,"doi":"10.1002\u002Fmma.9287","slug":"ulam-hyers-stability-of-fractional-ito-doob-2NwwvDdJ","type":"journal-article","title":"Ulam–Hyers stability of fractional Itô–Doob stochastic differential equations","abstract":"This article is devoted to prove the existence and uniqueness (EU) of solution of fractional Itô–Doob stochastic differential equations (FIDSDE) with order \n by using the fixed point technique (FPT). We analyze the Ulam–Hyers stability (UHS) of FIDSDE by using the Gronwall inequality (GI) and the stochastic analysis techniques. We present an application of our results by two theoretical examples.","authors":[{"family":"Mchiri","given":"Lassaad","affiliation":"University of Sfax","authorSlug":"lassaad-mchiri-jgxp6J","authorName":"Lassaad Mchiri","authorID":"17422181","authorLastKnownAffiliationId":161514,"authorSequenceNumber":1,"affiliationSlug":"university-of-sfax-n1P","affiliationID":"377"}],"keywords":["fixed point technique","fractional calculus","fractional Itô–Doob","Gronwall inequality","stochastic differential equations","Ulam–Hyers stability"],"year":2023,"shortJournal":"Math Methods in App Sciences","publisher":"Wiley","issue":"13","volume":"46","page":"13731-13740","memberId":311,"issns":["0170-4214","1099-1476"],"editorialNotices":[],"journalSlug":"mathematical-methods-in-the-applied-y808a","journal":"Mathematical Methods in the Applied Sciences","preprintLinks":[],"publicationLinks":[],"normalizedTypes":["article"]},"10.1002\u002Foca.2805":{"id":11185524796,"doi":"10.1002\u002Foca.2805","slug":"optimal-controls-for-fractional-stochastic-MVbkRylX","type":"journal-article","title":"Optimal controls for fractional stochastic differential systems driven by Rosenblatt process with impulses","abstract":"The objective of this article is to consider a new class of fractional stochastic differential systems driven by the Rosenblatt process with impulses. We used fractional calculus, stochastic analysis, and Krasnoselskii's fixed point theorem to study the existence of piecewise continuous mild solutions for the proposed system. Further, we discussed the existence of optimal controls for the considered system. Our main results are well supported by an illustrative example.","authors":[{"family":"Dhayal","given":"Rajesh","affiliation":"Thapar Institute of Engineering & Technology","authorSlug":"rajesh-dhayal-j60K05","authorName":"Rajesh Dhayal","authorID":"8817237","authorLastKnownAffiliationId":7023,"authorSequenceNumber":1,"affiliationSlug":"thapar-institute-of-engineering-Jaww","affiliationID":"7023"},{"family":"Gómez-Aguilar","given":"J. F.","affiliation":"Centro Nacional de Investigación y Desarrollo Tecnológico","authorSlug":"j-f-gomez-aguilar-W836An","authorName":"J. F. 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l=function(r,e,o){a.call(this,r,e&&e._rollbar_wrapped||e,o)};l._rollbarOldRemove=a,l.belongsToShim=o,e.removeEventListener=l}}r.exports={captureUncaughtExceptions:o,captureUnhandledRejections:t,wrapGlobals:a}},function(r,e){"use strict";function o(r,e){this.impl=r(e,this),this.options=e,n(o.prototype)}function n(r){for(var e=function(r){return function(){var e=Array.prototype.slice.call(arguments,0);if(this.impl[r])return this.impl[r].apply(this.impl,e)}},o="log,debug,info,warn,warning,error,critical,global,configure,handleUncaughtException,handleUnhandledRejection,_createItem,wrap,loadFull,shimId,captureEvent,captureDomContentLoaded,captureLoad".split(","),n=0;n<o.length;n++)r[o[n]]=e(o[n])}o.prototype._swapAndProcessMessages=function(r,e){this.impl=r(this.options);for(var o,n,t;o=e.shift();)n=o.method,t=o.args,this[n]&&"function"==typeof this[n]&&("captureDomContentLoaded"===n||"captureLoad"===n?this[n].apply(this,[t[0],o.ts]):this[n].apply(this,t));return this},r.exports=o},function(r,e){"use strict";r.exports=function(r){return function(e){if(!e&&!window._rollbarInitialized){r=r||{};for(var o,n,t=r.globalAlias||"Rollbar",a=window.rollbar,l=function(r){return new a(r)},i=0;o=window._rollbarShims[i++];)n||(n=o.handler),o.handler._swapAndProcessMessages(l,o.messages);window[t]=n,window._rollbarInitialized=!0}}}}]);
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