Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space

Ankit Kumar; Kamal Jeet; Ramesh Kumar Vats

doi:10.3934/eect.2021016

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2022, Volume 11, Issue 2: 605-619. Doi: 10.3934/eect.2021016

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Controllability of Hilfer fractional integro-differential equations of Sobolev-type with a nonlocal condition in a Banach space

Department of Mathematics & Scientific Computing, National Institute of Technology, Hamirpur (H.P.)-177005, India

^* Corresponding author: Kamal Jeet (kamaljeetp2@gmail.com)
^* Corresponding author: Kamal Jeet (kamaljeetp2@gmail.com)

Received: December 31, 2019

Revised: July 31, 2020

Early access: April 2021

Published: April 2022

The second and third author are supported by CSIR, India under Research Project no-25(0268)/17/EMR-II

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Abstract

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 $ \{P(t), \; t\geq0\} $ generated by the operators $ A $ and $ R $. For proving the main result we do not impose any condition on the relation between the domain of the operators $ A $ and $ R $. We also do not assume that the operator $ R $ 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.

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Mathematics Subject Classification: Primary: 34G20, 34K30, 93B05.

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