AccScience Publishing / IJOCTA / Volume 14 / Issue 1 / DOI: 10.11121/ijocta.1428
RESEARCH ARTICLE

Controllability of nonlinear fractional integrodifferential systems involving multiple delays in control

Abdul Haq1* Nagarajan Sukavanam2
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1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India
2 Department of Mathematicsn Institute of Technology, Roorkee, Roorkee, Uttarakhand, India
IJOCTA 2024, 14(1), 1–11; https://doi.org/10.11121/ijocta.1428
Submitted: 12 July 2023 | Accepted: 18 October 2023 | Published: 7 January 2024
© 2024 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

This work studies the existence of solutions and approximate controllability of fractional integrodifferential systems with Riemann-Liouville derivatives and with multiple delays in control. We establish suitable assumptions to prove the existence of solutions. Controllability of the system is shown by assuming a range condition on control operators and Lipschitz condition on non-linear functions. We use the concepts of strongly continuous semigroup rather than resolvent operators. Finally, an example is give to illustrate the theory.

Keywords
Fractional derivative
Delay system
Mild solution
null-controllability
Conflict of interest
The authors declare they have no competing interests.
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