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- Title
Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse.
- Authors
Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, Varshini; Baleanu, Dumitru
- 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.
- Subjects
INTEGRO-differential equations; EXPONENTIAL stability; HAUSDORFF measures; RESOLVENTS (Mathematics); HILBERT space
- Publication
Journal of Inequalities & Applications, 2023, Vol 2023, Issue 1, p1
- ISSN
1025-5834
- Publication type
Article
- DOI
10.1186/s13660-023-03023-y