Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse
Abstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-03023-y |
| _version_ | 1797451164711649280 |
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| author | Ramkumar Kasinathan Ravikumar Kasinathan Varshini Sandrasekaran Dumitru Baleanu |
| author_facet | Ramkumar Kasinathan Ravikumar Kasinathan Varshini Sandrasekaran Dumitru Baleanu |
| author_sort | Ramkumar Kasinathan |
| collection | DOAJ |
| description | Abstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Mönch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results. |
| first_indexed | 2024-03-09T14:49:53Z |
| format | Article |
| id | doaj.art-fcbd72f147514f01a696121d5028257f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-03-09T14:49:53Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-fcbd72f147514f01a696121d5028257f2023-11-26T14:32:41ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-09-012023111910.1186/s13660-023-03023-yExistence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulseRamkumar Kasinathan0Ravikumar Kasinathan1Varshini Sandrasekaran2Dumitru Baleanu3Department of Mathematics, PSG College of Arts & ScienceDepartment of Mathematics, PSG College of Arts & ScienceDepartment of Mathematics, Sri Eshwar College of EngineeringDepartment of Mathematics, Cankaya UniversityAbstract The theoretical approach of random impulsive stochastic integrodifferential equations (RISIDEs) with finite delay, noncompact semigroups, and resolvent operators in Hilbert space is investigated in this article. Initially, a random impulsive stochastic integrodifferential system is proposed and the existence of a mild solution for the system is established using the Mönch fixed-point theorem and contemplating Hausdorff measures of noncompactness. Then, the stability results including a continuous dependence of solutions on initial conditions, exponential stability, and Hyers–Ulam stability for the aforementioned system are investigated. Finally, an example is proposed to validate the obtained results.https://doi.org/10.1186/s13660-023-03023-yStochastic differential equationsRandom impulseNoncompact semigroupHyers–Ulam stabilityMean-square exponential stability |
| spellingShingle | Ramkumar Kasinathan Ravikumar Kasinathan Varshini Sandrasekaran Dumitru Baleanu Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse Journal of Inequalities and Applications Stochastic differential equations Random impulse Noncompact semigroup Hyers–Ulam stability Mean-square exponential stability |
| title | Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse |
| title_full | Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse |
| title_fullStr | Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse |
| title_full_unstemmed | Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse |
| title_short | Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse |
| title_sort | existence and hyers ulam stability of stochastic integrodifferential equations with a random impulse |
| topic | Stochastic differential equations Random impulse Noncompact semigroup Hyers–Ulam stability Mean-square exponential stability |
| url | https://doi.org/10.1186/s13660-023-03023-y |
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