Page 109 - IJOCTA-15-1

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.2, pp.103-122 (2025)
https://doi.org/10.36922/ijocta.1524

RESEARCH ARTICLE

Exponential stability for higher-order impulsive fractional neutral
stochastic integro-delay differential equations with mixed brownian
motions and non-local conditions

2
2*
1
Dhanalakshmi Kasinathan , Ramkumar Kasinathan , Ravikumar Kasinathan ,
Dimplekumar Chalishajar 3
1
Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram - 624
302, Tamil Nadu, India
2
Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641014, Tamil Nadu, India
3
Department of Applied Mathematics, Mallory Hall, Virginia Military Institute (VMI), Lexington, VA 24450,
USA
dlriya20@gmail.com, ramkumarkpsg@gmail.com, ravikumarkpsg@gmail.com, chalishajardn@vmi.edu

ARTICLE INFO ABSTRACT
Article History: This paper investigates the exponential stability of second-order fractional neu-
Received: 7 January 2024 tral stochastic integral-delay differential equations (FNSIDDEs) with impulses
Accepted: 28 May 2024 driven by mixed fractional Brownian motions (fBm). Existence and uniqueness
Available Online: 24 January 2025 conditions ensure that FNSIDDEs are acquired by formulating a Banach fixed
Keywords: point theorem (BFPT). Novel sufficient conditions have to prove p th moment
Exponential stability exponential stability of FNSIDDEs via fBm employing the impulsive-integral
Fractional Brownian motion inequality. The current study expands and improves on previous findings. Ad-
Stochastic integro-delay ditionally, an example is presented to illustrate the efficiency of the obtained
differential equations theoretical results.
Impulsive-integral inequality
Fixed point theorem
AMS Classification 2010:
26A33; 34A08; 35H15; 34K50
47H10; 60H10

1. Introduction (FSDEs) with random perturbations have been
applied as the mathematical models of many prac-
Fractional calculus (FC) has its applications in tical scenarios. 5–8 This motivates researchers to
several mathematical, physical, and engineering move from fractional deterministic models to frac-
sciences. It’s a generalized the ideas of integer or- tional stochastic models to guarantee the model
der differentiation. 1–4 It describes the dynamical performance. The most important advantage of
behavior of the models more accurately than the utilizing differential equations of fractional or-
integer-order equations because of their heredi- der in the applications is their nonlocal property.
tary properties. The increasing interest in frac- This implies that the system state depends not
tional equations is motivated by the applications only upon its current state but also upon all of its
in various fields of science such as physics, fluid histories. A variety of problems arising in elastic-
mechanics, heat conduction in materials with ity theory, molecular dynamics, and quantum me-
memory, electromagnetism, and engineering. chanics can be described in general by a second-
Recently, random fluctuations have appeared order nonlinear SDEs, see. 9–15 Due to this reason,
commonly in various natural and synthetic sys- many researchers’ are focused on second-order dif-
tems. Fractional stochastic differential equations ferential equations. Integro-differential equations
*Corresponding Author
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