Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses
This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we t...
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2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011736 |
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| author | Hasanen A. Hammad Manuel De la Sen |
| author_facet | Hasanen A. Hammad Manuel De la Sen |
| author_sort | Hasanen A. Hammad |
| collection | DOAJ |
| description | This paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example. |
| format | Article |
| id | doaj-art-5f2220d95364488fbaab88c6e2365e6c |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-5f2220d95364488fbaab88c6e2365e6c2025-01-18T05:03:34ZengElsevierAlexandria Engineering Journal1110-01682025-01-01111306328Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulsesHasanen A. Hammad0Manuel De la Sen1Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia; Corresponding author.Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940, Leioa Bizkaia, SpainThis paper investigates the existence and approximate controllability (ACA) of fractional neutral-type stochastic differential inclusions (NTSDIs) characterized by non-instantaneous impulses within a separable Hilbert space (HS) framework. Employing the Atangana–Baleanu–Caputo (ABC) derivative, we transform the system into an equivalent fixed-point (FP) problem through an integral operator. Subsequently, the Bohnenblust–Karlin FP theorem is leveraged to establish existence results. By assuming ACA of the corresponding linear system, we derive sufficient conditions for the ACA of the nonlinear stochastic impulsive control system. Our analysis relies on concepts from stochastic analysis, fractional calculus, FP theory, semigroup theory, and the theory of multivalued maps (MVMs). The theoretical findings are illustrated through a concrete example.http://www.sciencedirect.com/science/article/pii/S1110016824011736Bohnenblust–Karlin FP approachesStochastic systemsApproximate controllabilityFractional derivativesNonlinear equations |
| spellingShingle | Hasanen A. Hammad Manuel De la Sen Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses Alexandria Engineering Journal Bohnenblust–Karlin FP approaches Stochastic systems Approximate controllability Fractional derivatives Nonlinear equations |
| title | Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses |
| title_full | Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses |
| title_fullStr | Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses |
| title_full_unstemmed | Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses |
| title_short | Existence of a mild solution and approximate controllability for fractional random integro-differential inclusions with non-instantaneous impulses |
| title_sort | existence of a mild solution and approximate controllability for fractional random integro differential inclusions with non instantaneous impulses |
| topic | Bohnenblust–Karlin FP approaches Stochastic systems Approximate controllability Fractional derivatives Nonlinear equations |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011736 |
| work_keys_str_mv | AT hasanenahammad existenceofamildsolutionandapproximatecontrollabilityforfractionalrandomintegrodifferentialinclusionswithnoninstantaneousimpulses AT manueldelasen existenceofamildsolutionandapproximatecontrollabilityforfractionalrandomintegrodifferentialinclusionswithnoninstantaneousimpulses |