Open AccessControllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space
Author(s) -
Ankit Kumar,
Kamal Jeet,
Ramesh Kumar Vats
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2021016
Subject(s) - mathematics , sobolev space , banach space , type (biology) , bounded function , fixed point theorem , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , ecology , biology
This paper aims to establish sufficient conditions for the exact controllability of the nonlocal Hilfer fractional integro-differential system of Sobolev-type using the theory of propagation family \begin{document}$ \{P(t), \; t\geq0\} $\end{document} generated by the operators \begin{document}$ A $\end{document} and \begin{document}$ R $\end{document} . For proving the main result we do not impose any condition on the relation between the domain of the operators \begin{document}$ A $\end{document} and \begin{document}$ R $\end{document} . We also do not assume that the operator \begin{document}$ R $\end{document} has necessarily a bounded inverse. The main tools applied in our analysis are the theory of measure of noncompactness, fractional calculus, and Sadovskii's fixed point theorem. Finally, we provide an example to show the application of our main result.