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] |
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| Database: | Engineering Source |
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| 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] |
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| ISSN: | 27305422 |
| DOI: | 10.1186/s13663-026-00825-9 |
