Existence and Hyers–Ulam stability of stochastic integrodifferential equations with a random impulse

Autor:	Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran, Dumitru Baleanu
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Stochastic differential equations Random impulse Noncompact semigroup Hyers–Ulam stability Mean-square exponential stability Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2023, Iss 1, Pp 1-19 (2023)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-023-03023-y
Popis:	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.
Databáze:	Directory of Open Access Journals
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