Page 111 - IJOCTA-15-3

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.3, pp.483-492 (2025)
https://doi.org/10.36922/ijocta.7118

RESEARCH ARTICLE

Trajectory controllability of integro-differential system of fractional
orders in Hilbert spaces

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Urvashi Arora , Sachin Singh , V. Vijayakumar , and Anurag Shukla 4*
1
Manhattan University, Manhattan College Pkwy, Bronx, New York, United States of America
2
Department of Electrical Engineering, IET Lucknow, India
3
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore,
Tamilnadu, India
4
Department of Applied Sciences and Humanities, Rajkiya Engineering College Kannauj, Kannauj, India
urvashiaroraiitr@gmail.com, sachinsingh@ietlucknow.ac.in, vijaysarovel@gmail.com,
anuragshukla259@gmail.com
ARTICLE INFO ABSTRACT

Article History: The trajectory controllability for fractional order semilinear integrodifferen-
Received: December 19, 2024 tial systems of order ν ∈ (0, 1] and ν ∈ (1, 2] is the subject of this paper.
1st revised: March 22, 2025 Monotonicity is an important characteristic in many communications applica-
2nd revised: April 17, 2025 tions in which digital-to-analog converter circuits are used. Such applications
3rd revised: May 6, 2025 can function in the presence of nonlinearity, but not in the presence of non-
Accepted: May 7, 2025 monotonicity. Therefore, it becomes quite interesting to study a problem as-
Published Online: May 30, 2025 suming the monotonicity of the nonlinear function. With the help of fractional
Keywords: calculus, adequate conditions have been developed to verify the trajectory con-
Trajectory controllability trollability for fractional order semilinear integrodifferential system using the
Fractional order system basics of monotone nonlinearity and coercivity. Finally, some examples are
Integrodifferential system presented to demonstrate the viability of the acquired results.
Subject Classification 2020:
93B05, 93C10

1. Introduction and design of control systems. These kinds of is-
sues can be determined with various signification
of fractional derivatives. It has different applica-
The principles of fractional calculus and the frac- tions in separate fields, for example, economics,
tional differential equation have dominated math- the control of chemical outgrowths, biology, power
ematics in recent decades. Some physical prob- systems, space technology, engineering, electron-
lems cannot be solved using differential equations ics, physics, robotics, transportation, chemistry,
of integer order, but they can be solved using and so on; the solution of these types of seeds
differential equations of fractional order. As a has become a significant work for young scholars.
result, numerous academics have recently made Controllability research, which was conceived by
significant contributions to the fields of electro- Kalman, began in earnest at the beginning of the
magnetics, control theory, signal, porous media, 1960s. Since then, several studies have been con-
viscoelasticity, biological, engineering difficulties, ducted utilizing various methodologies in the set-
image processing, fluid flow, diffusion, theology, ting of finite and infinite dimensional determin-
and other fields. The notation of optimal controls istic and stochastic systems, one can refer Arora
1
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has performed as an important tool in analysis and Sukavanam, Bragdi and Hazi, Davison and
*Corresponding Author
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