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

被引：0

作者：

Alnemer, Ghada ^{[1
]}

Hosny, Mohamed ^{[2
]}

Udhayakumar, Ramalingam ^{[3
]}

Elshenhab, Ahmed M. ^{[4
]}

机构：

[1] Princess Nourah Bint Abdulrahman Univ, Coll Sci, Dept Math Sci, POB 84428, Riyadh 11671, Saudi Arabia

[2] Benha Univ, Benha Fac Engn, Dept Elect Engn, Banha 13511, Egypt

[3] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore 632014, India

[4] Mansoura Univ, Fac Sci, Dept Math, Mansoura 35516, Egypt

来源：

FRACTAL AND FRACTIONAL | 2024年 / 8卷 / 06期

关键词：

well-posedness; Hyers-Ulam stability; fractional stochastic delay system; Rosenblatt process; delayed Mittag-Leffler matrix function; Krasnoselskii's fixed point theorem; DIFFERENTIAL-EQUATIONS; APPROXIMATE CONTROLLABILITY; EXISTENCE; DRIVEN;

D O I：

10.3390/fractalfract8060342

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 & ouml;nwall's inequality, sufficient criteria for Hyers-Ulam stability are established. Ultimately, an example is presented to demonstrate the effectiveness of the obtained findings.

引用

页数：15

共 38 条

[1] Ulam-Hyers stability of Caputo type fractional stochastic neutral differential equations [J].

Ahmadova, Arzu ;

Mahmudov, Nazim, I .

STATISTICS & PROBABILITY LETTERS, 2021, 168

[2] Semilinear Neutral Fractional Stochastic Integro-Differential Equations with Nonlocal Conditions [J].

Ahmed, Hamdy M. .

JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (02) :667-680

[3] Discussion on the Approximate Controllability of Hilfer Fractional Neutral Integro-Differential Inclusions via Almost Sectorial Operators [J].

Bose, Chandrabose Sindhu Varun ;

Udhayakumar, Ramalingam ;

Elshenhab, Ahmed M. ;

Kumar, Marappan Sathish ;

Ro, Jong-Suk .

FRACTAL AND FRACTIONAL, 2022, 6 (10)

[4] Mechanics with variable-order differential operators [J].

Coimbra, CFM .

ANNALEN DER PHYSIK, 2003, 12 (11-12) :692-703

[5]

Da Prato G., 2014, Encyclopedia of Mathematics and its Applications, V2nd edn, DOI DOI 10.1017/CBO9781107295513

[6] Existence and stability for fractional parabolic integro-partial differential equations with fractional Brownian motion and nonlocal condition [J].

El-Borai, M. M. ;

El-Nadi, K. El-S. ;

Ahmed, H. M. ;

El-Owaidy, H. M. ;

Ghanem, A. S. ;

Sakthivel, R. .

COGENT MATHEMATICS & STATISTICS, 2018, 5 (01)

[7] On some fractional stochastic delay differential equations [J].

El-Borai, Mahmoud M. ;

El-Nadi, Khairia El-Said ;

Fouad, Hoda A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (03) :1165-1170

[8] Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay [J].

Elshenhab, Ahmed M. ;

Wang, Xingtao ;

Mofarreh, Fatemah ;

Bazighifan, Omar .

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, 2023, 134 (02) :927-940

[9] Controllability and Hyers-Ulam Stability of Differential Systems with Pure Delay [J].

Elshenhab, Ahmed M. ;

Wang, Xingtao .

MATHEMATICS, 2022, 10 (08)

[10] Representation of solutions for linear fractional systems with pure delay and multiple delays [J].

Elshenhab, Ahmed M. ;

Wang, Xing Tao .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (17) :12835-12850

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