Results on the Approximate Controllability of Hilfer Type fractional Semilinear Control Systems

The approximate controllability of Hilfer fractional semilinear control systems is the main focus of this study. Two distinct kinds of necessary requirements have been investigated. For the first set of results, we use Schauder’s fixed point techniques, compactness of the relevant fractional operato...

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Published inQualitative theory of dynamical systems Vol. 22; no. 2
Main Authors Vijayakumar, V., Malik, Muslim, Shukla, Anurag
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2023
Springer Nature B.V
Subjects
Control systems
Controllability
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Operators (mathematics)
Fixed point techniques
34G10
93B05
Gronwall’s inequality
Controllability
Hilfer fractional differential equations
34G25
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Summary:The approximate controllability of Hilfer fractional semilinear control systems is the main focus of this study. Two distinct kinds of necessary requirements have been investigated. For the first set of results, we use Schauder’s fixed point techniques, compactness of the relevant fractional operator, and concepts on fractional derivative to obtain them. Utilizing the Gronwall’s inequality in the second set, we are able to demonstrate the main points without using the corresponding fractional operator’s compactness or the fixed point method. Also provided is a case study for the validation of theoretical findings.
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ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-023-00759-2