Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process
The purpose of this paper is to determine a class of neutral stochastic functional integro-differential system in real separable Hilbert spaces as well as the exponential stability results. The Rosenblatt process acts as the driving force behind the systems. Initially, the existence results for mild...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-05-01
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| Series: | Results in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2590037423000122 |
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| author | Ravikumar Kasinathan Ramkumar Kasinathan Dimplekumar Chalishajar Varshini Sandrasekaran Sonal Jain |
| author_facet | Ravikumar Kasinathan Ramkumar Kasinathan Dimplekumar Chalishajar Varshini Sandrasekaran Sonal Jain |
| author_sort | Ravikumar Kasinathan |
| collection | DOAJ |
| description | The purpose of this paper is to determine a class of neutral stochastic functional integro-differential system in real separable Hilbert spaces as well as the exponential stability results. The Rosenblatt process acts as the driving force behind the systems. Initially, the existence results for mild solutions of the stochastic system is investigated by using stochastic analysis, integro-differential theory, and fixed point theory. The analysis of the exponential stability of mild solutions to nonlinear neutral stochastic integro-differential systems driven by Rosenblatt process is the main objective of the investigation’s further stages. The system’s trajectory controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. Our work extends the work of Chalishajar et al. (2010), Chalishajar and Chalishajar (2015), Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022) where the pth moment exponential stability has not discussed. Also, numerical simulation has not studied in Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022). |
| first_indexed | 2024-03-13T08:24:14Z |
| format | Article |
| id | doaj.art-d3604251b99040bcb7e70da8bef18cdc |
| institution | Directory Open Access Journal |
| issn | 2590-0374 |
| language | English |
| last_indexed | 2024-03-13T08:24:14Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Applied Mathematics |
| spelling | doaj.art-d3604251b99040bcb7e70da8bef18cdc2023-05-31T04:47:32ZengElsevierResults in Applied Mathematics2590-03742023-05-0118100366Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt processRavikumar Kasinathan0Ramkumar Kasinathan1Dimplekumar Chalishajar2Varshini Sandrasekaran3Sonal Jain4Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, IndiaDepartment of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, IndiaDepartment of Applied Mathematics, Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450, USA; Corresponding author.Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, IndiaDepartment of Mathematical Sciences, UAE University, 15551 Al-Ain, United Arab EmiratesThe purpose of this paper is to determine a class of neutral stochastic functional integro-differential system in real separable Hilbert spaces as well as the exponential stability results. The Rosenblatt process acts as the driving force behind the systems. Initially, the existence results for mild solutions of the stochastic system is investigated by using stochastic analysis, integro-differential theory, and fixed point theory. The analysis of the exponential stability of mild solutions to nonlinear neutral stochastic integro-differential systems driven by Rosenblatt process is the main objective of the investigation’s further stages. The system’s trajectory controllability is then examined using Gronwall’s inequality. An example is given to validate the results at the end. Our work extends the work of Chalishajar et al. (2010), Chalishajar and Chalishajar (2015), Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022) where the pth moment exponential stability has not discussed. Also, numerical simulation has not studied in Chalishajar et al. (2023), Muslim and George (2019) and Durga et al. (2022).http://www.sciencedirect.com/science/article/pii/S2590037423000122Resolvent operatorTrajectory controllabilityExponential stabilityRosenblatt processInfinite delayStochastic functional integro-differential equation |
| spellingShingle | Ravikumar Kasinathan Ramkumar Kasinathan Dimplekumar Chalishajar Varshini Sandrasekaran Sonal Jain Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process Results in Applied Mathematics Resolvent operator Trajectory controllability Exponential stability Rosenblatt process Infinite delay Stochastic functional integro-differential equation |
| title | Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process |
| title_full | Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process |
| title_fullStr | Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process |
| title_full_unstemmed | Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process |
| title_short | Trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by Rosenblatt process |
| title_sort | trajectory control and pth moment exponential stability of neutral functional stochastic systems driven by rosenblatt process |
| topic | Resolvent operator Trajectory controllability Exponential stability Rosenblatt process Infinite delay Stochastic functional integro-differential equation |
| url | http://www.sciencedirect.com/science/article/pii/S2590037423000122 |
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