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

Ghada AlNemer; Mohamed Hosny; Ramalingam Udhayakumar; Ahmed M. Elshenhab

doi:10.3390/fractalfract8060342

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

Ghada AlNemer
, Mohamed Hosny
, Ramalingam Udhayakumar
, Ahmed M. Elshenhab^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Article number	342
Journal	Fractal and Fractional
Volume	8
Issue number	6
DOIs	https://doi.org/10.3390/fractalfract8060342
State	Published - Jun 2024
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2024 by the authors.

Keywords

Hyers–Ulam stability
Krasnoselskii’s fixed point theorem
Rosenblatt process
delayed Mittag–Leffler matrix function
fractional stochastic delay system
well-posedness

ASJC Scopus subject areas

Analysis
Statistical and Nonlinear Physics
Statistics and Probability

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10.3390/fractalfract8060342

Cite this

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

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 Gr{\"o}nwall{\textquoteright}s inequality, sufficient criteria for Hyers–Ulam stability are established. Ultimately, an example is presented to demonstrate the effectiveness of the obtained findings.",

keywords = "Hyers–Ulam stability, Krasnoselskii{\textquoteright}s fixed point theorem, Rosenblatt process, delayed Mittag–Leffler matrix function, fractional stochastic delay system, well-posedness",

author = "Ghada AlNemer and Mohamed Hosny and Ramalingam Udhayakumar and Elshenhab, \{Ahmed M.\}",

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month = jun,

doi = "10.3390/fractalfract8060342",

language = "English",

volume = "8",

journal = "Fractal and Fractional",

issn = "2504-3110",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

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T1 - Well-Posedness and Hyers–Ulam Stability of Fractional Stochastic Delay Systems Governed by the Rosenblatt Process

AU - AlNemer, Ghada

AU - Hosny, Mohamed

AU - Udhayakumar, Ramalingam

AU - Elshenhab, Ahmed M.

PY - 2024/6

Y1 - 2024/6

N2 - 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.

AB - 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.

KW - Hyers–Ulam stability

KW - Krasnoselskii’s fixed point theorem

KW - Rosenblatt process

KW - delayed Mittag–Leffler matrix function

KW - fractional stochastic delay system

KW - well-posedness

UR - https://www.scopus.com/pages/publications/85196902174

U2 - 10.3390/fractalfract8060342

DO - 10.3390/fractalfract8060342

M3 - Article

AN - SCOPUS:85196902174

SN - 2504-3110

VL - 8

JO - Fractal and Fractional

JF - Fractal and Fractional

IS - 6

M1 - 342

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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