Approximate controllability of fractional stochastic differential equations with Hilfer derivative: insights from multivalued maps and fixed-point method.
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| Title: | Approximate controllability of fractional stochastic differential equations with Hilfer derivative: insights from multivalued maps and fixed-point method. |
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| Authors: | Niazi, Azmat Ullah Khan1 (AUTHOR) azmatullah.khan@math.uol.edu.pk, Alsinai, Ammar2,3 (AUTHOR) aliiammar1985@gmail.com, Yasmeen, Sadia1 (AUTHOR) sadia8033@gmail.com |
| Source: | Fixed Point Theory & Algorithms for Sciences & Engineering. Dec20262/11/2026, Vol. 2026 Issue 1, p1-25. 25p. |
| Subjects: | Controllability in systems engineering, Stochastic differential equations, Fixed point theory, Control theory (Engineering), Fractional calculus, Stochastic systems, Set-valued maps |
| Abstract: | The aim of this paper is to investigate the approximate controllability of fractional stochastic differential equations involving the Hilfer derivative of order 1 < μ < 2 and type ν ∈ [ 0 , 1 ]. The analysis is carried out within the framework of fractional calculus, where the existence of mild solutions is established by employing properties of multivalued maps together with fixed-point methods. Initially, we study the approximate controllability of the considered stochastic system, and subsequently, an illustrative application is provided to demonstrate the effectiveness of the proposed approach and validate the theoretical results. Unlike existing studies that mainly address deterministic systems or stochastic models with Caputo-type derivatives, this work considers Hilfer-type stochastic evolution equations with multivalued control operators. By combining measurable selection techniques, Mainardi/Wright kernel representations, and a β-regularized controllability operator, we obtain new mean-square approximate controllability results not covered in the current literature. [ABSTRACT FROM AUTHOR] |
| Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 192414782 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Approximate controllability of fractional stochastic differential equations with Hilfer derivative: insights from multivalued maps and fixed-point method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Niazi%2C+Azmat+Ullah+Khan%22">Niazi, Azmat Ullah Khan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> azmatullah.khan@math.uol.edu.pk</i><br /><searchLink fieldCode="AR" term="%22Alsinai%2C+Ammar%22">Alsinai, Ammar</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> aliiammar1985@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Yasmeen%2C+Sadia%22">Yasmeen, Sadia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sadia8033@gmail.com</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Fixed+Point+Theory+%26+Algorithms+for+Sciences+%26+Engineering%22">Fixed Point Theory & Algorithms for Sciences & Engineering</searchLink>. Dec20262/11/2026, Vol. 2026 Issue 1, p1-25. 25p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Controllability+in+systems+engineering%22">Controllability in systems engineering</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+differential+equations%22">Stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Fixed+point+theory%22">Fixed point theory</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink><br /><searchLink fieldCode="DE" term="%22Set-valued+maps%22">Set-valued maps</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The aim of this paper is to investigate the approximate controllability of fractional stochastic differential equations involving the Hilfer derivative of order 1 < μ < 2 and type ν ∈ [ 0 , 1 ]. The analysis is carried out within the framework of fractional calculus, where the existence of mild solutions is established by employing properties of multivalued maps together with fixed-point methods. Initially, we study the approximate controllability of the considered stochastic system, and subsequently, an illustrative application is provided to demonstrate the effectiveness of the proposed approach and validate the theoretical results. Unlike existing studies that mainly address deterministic systems or stochastic models with Caputo-type derivatives, this work considers Hilfer-type stochastic evolution equations with multivalued control operators. By combining measurable selection techniques, Mainardi/Wright kernel representations, and a β-regularized controllability operator, we obtain new mean-square approximate controllability results not covered in the current literature. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1186/s13663-026-00825-9 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 1 Subjects: – SubjectFull: Controllability in systems engineering Type: general – SubjectFull: Stochastic differential equations Type: general – SubjectFull: Fixed point theory Type: general – SubjectFull: Control theory (Engineering) Type: general – SubjectFull: Fractional calculus Type: general – SubjectFull: Stochastic systems Type: general – SubjectFull: Set-valued maps Type: general Titles: – TitleFull: Approximate controllability of fractional stochastic differential equations with Hilfer derivative: insights from multivalued maps and fixed-point method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Niazi, Azmat Ullah Khan – PersonEntity: Name: NameFull: Alsinai, Ammar – PersonEntity: Name: NameFull: Yasmeen, Sadia IsPartOfRelationships: – BibEntity: Dates: – D: 11 M: 02 Text: Dec20262/11/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 27305422 Numbering: – Type: volume Value: 2026 – Type: issue Value: 1 Titles: – TitleFull: Fixed Point Theory & Algorithms for Sciences & Engineering Type: main |
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