Existence and Hyers–Ulam Stability of Stochastic Delay Systems Governed by the Rosenblatt Process

Ghada AlNemer, Mohamed Hosny, Ramalingam Udhayakumar and Ahmed M. Elshenhab ()
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Ghada AlNemer: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mohamed Hosny: Department of Electrical Engineering, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt
Ramalingam Udhayakumar: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India
Ahmed M. Elshenhab: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2024, vol. 12, issue 11, 1-15

Abstract: Under the effect of the Rosenblatt process, time-delay systems of nonlinear stochastic delay differential equations are considered. Utilizing the delayed matrix functions and exact solutions for these systems, the existence and Hyers–Ulam stability results are derived. First, depending on the fixed point theory, the existence and uniqueness of solutions are proven. Next, sufficient criteria for the Hyers–Ulam stability are established. Ultimately, to illustrate the importance of the results, an example is provided.

Keywords: Hyers–Ulam stability; stochastic delay system; Rosenblatt process; delayed matrix function; Krasnoselskii’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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