On the qualitative behaviors of stochastic delay integro-differential equations of second order

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Mahmoud A. M., Tunç C.

Journal of Inequalities and Applications, vol.2024, no.1, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2024 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1186/s13660-024-03085-6
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: 34C11, 34D20, 34K20, 34K50, 60H35, Boundedness, Continuity, Integro-differential equation, Lyapunov functional, Stability, Stochastic delay
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature.