Well-Posedness and Hyers–Ulam Stability of Fractional Stochastic Delay Systems Governed by the Rosenblatt Process-Reference-Cited by-同舟云学术

Well-Posedness and Hyers–Ulam Stability of Fractional Stochastic Delay Systems Governed by the Rosenblatt Process

Published:2024-06-06 Issue:6 Volume:8 Page:342
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

AlNemer Ghada¹^ORCID,Hosny Mohamed²^ORCID,Udhayakumar Ramalingam³^ORCID,Elshenhab Ahmed M.⁴^ORCID

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Electrical Engineering, Benha Faculty of Engineering, Benha University, Benha 13511, Egypt

3. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, India

4. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Abstract

Under the effect of the Rosenblatt process, the well-posedness and Hyers–Ulam stability of nonlinear fractional stochastic delay systems are considered. First, depending on fixed-point theory, the existence and uniqueness of solutions are proven. Next, utilizing the delayed Mittag–Leffler matrix functions and Grönwall’s inequality, sufficient criteria for Hyers–Ulam stability are established. Ultimately, an example is presented to demonstrate the effectiveness of the obtained findings.

Funder

Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/6/342/pdf

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