A note on the approximate controllability of second-order integro-differential evolution control systems via resolvent operators

The approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and L...

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Bibliographic Details
Published in:Advances in difference equations 2021-11, Vol.2021 (1), p.1-13, Article 484
Main Authors: Vijayakumar, Velusamy, Shukla, Anurag, Nisar, Kottakkaran Sooppy, Jamshed, Wasim, Rezapour, Shahram
Format: Article
Language:English
Subjects:
Analysis
Approximate controllability
Banach spaces
Control systems
Control theory
Controllability
Difference and Functional Equations
Evolution
Evolutionary computation
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Fixed points (mathematics)
Functional Analysis
Gronwall’s inequality
Hilbert space
Lipschitz condition
Mathematical functions
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Resolvent operators
Second-order integro-differential systems
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Summary:The approximate controllability of second-order integro-differential evolution control systems using resolvent operators is the focus of this work. We analyze approximate controllability outcomes by referring to fractional theories, resolvent operators, semigroup theory, Gronwall’s inequality, and Lipschitz condition. The article avoids the use of well-known fixed point theorem approaches. We have also included one example of theoretical consequences that has been validated.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03639-8