Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2023; 38(3): 967-982

Online first article July 25, 2023      Printed July 31, 2023

https://doi.org/10.4134/CKMS.c220231

Copyright © The Korean Mathematical Society.

Hyers-Ulam stability of fractional stochastic differential equations with random impulse

Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran

China Medical University; PSG College of Arts and Science; PSG College of Arts and Science; PSG College of Arts and Science; Sri Eshwar College of Engineering

Abstract

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The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.

Keywords: Existence, stability, random impulse, fractional stochastic differential system, Kransnoselskii's fixed point theorem, Hyers-Ulam stability

MSC numbers: Primary 34A12, 37H60, 60H10, 47H30

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