Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

Avadhesh Kumar; Ankit Kumar; Ramesh Kumar Vats; Parveen Kumar

doi:10.3934/eect.2021058

Article Contents

2022, Volume 11, Issue 5: 1635-1654. Doi: 10.3934/eect.2021058

This issue Previous Article Impulsive hemivariational inequality for a class of history-dependent quasistatic frictional contact problems Next Article Controlled singular evolution equations and Pontryagin type maximum principle with applications

Approximate controllability of neutral delay integro-differential inclusion of order $ \alpha\in (1, 2) $ with non-instantaneous impulses

1.
Department of Mathematics & Computer Science, Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam (A.P.)-515134, India
2.
Department of Mathematics & Scientific Computing, National Institute of Technology, Hamirpur (H.P.)-177005, India

^* Corresponding author: Avadhesh Kumar (soni.iitkgp@gmail.com)
^* Corresponding author: Avadhesh Kumar (soni.iitkgp@gmail.com)

Received: May 31, 2021

Revised: August 31, 2021

Early access: November 2021

Published: October 2022

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Abstract

This paper aims to establish the approximate controllability results for fractional neutral integro-differential inclusions with non-instantaneous impulse and infinite delay. Sufficient conditions for approximate controllability have been established for the proposed control problem. The tools for study include the fixed point theorem for discontinuous multi-valued operators with the $ \alpha- $resolvent operator. Finally, the proposed results are illustrated with the help of an example.

Keywords:

Approximate controllability,
non-instantaneous impulses,
fractional neutral differential inclusions,
integro,
$ \alpha- $resolvent operator,
delay.

Mathematics Subject Classification: Primary: 93B05, 34A08, 34K45.

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