Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions

Dumitru Baleanu; Ramkumar Kasinathan; Ravikumar Kasinathan; Varshini Sandrasekaran; Dumitru Baleanu; Ramkumar Kasinathan; Ravikumar Kasinathan; Varshini Sandrasekaran

doi:10.3934/math.2023132

AIMS Mathematics

2023, Volume 8, Issue 2: 2556-2575. doi: 10.3934/math.2023132

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Research article

Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions

1.
Department of Mathematics, Cankaya University, 06530 Balgat, Ankara, Turkey
2.
Institute of Space sciences, Magyrele-Bucharest, Romania
3.
Department of Medical Research, China Medical University Hospital, China Medical, University, Taichung, Taiwan
4.
Department of Mathematics with Computer Applications, PSG College of Arts and Science, Coimbatore 641 046, India
5.
Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 046, India

Received: 06 August 2022 Revised: 14 October 2022 Accepted: 24 October 2022 Published: 07 November 2022
MSC : 35R12, 60H15

In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and M$ \ddot{o} $nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.
- stochastic differential equations,
- random impulse,
- Hyers-Ulam stability,
- mean-square exponential stability
Citation: Dumitru Baleanu, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran. Existence, uniqueness and Hyers-Ulam stability of random impulsive stochastic integro-differential equations with nonlocal conditions[J]. AIMS Mathematics, 2023, 8(2): 2556-2575. doi: 10.3934/math.2023132

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Abstract

In this article, we study the existence and stability results of mild solutions for random impulsive stochastic integro-differential equations (RISIDEs) with noncompact semigroups and resolvent operators in Hilbert spaces. Initially, we prove the existence of mild solutions using Hausdorff measures of noncompactness and M$ \ddot{o} $nch fixed point theorem. Then, we explore the stability results which includes continuous dependence of initial conditions, Hyers-Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, we propose an example to validate the obtained results.

References

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