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Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay

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An Erratum to this article was published on 04 June 2016

Abstract

In this paper, we obtain a set of sufficient conditions to prove the approximate controllability for a class of nonlocal neutral fractional integro-differential equations, with time varying delays, considered in a Hilbert space. We also establish the existence of a mild solution of the system. The main tools used in our analysis are the theory of analytic semigroups, the theory of fractional powers of operators, α-norm, fractional calculus, and Krasnoselskii’s fixed point theorem. An example is provided to illustrate the applicability of the main results.

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Acknowledgments

We would like to thank the referees for their valuable comments and suggestions which led to the improvement of the original manuscript. The first author would like to thank the UGC of India for support to this work. The second author would like to acknowledge that this work has been carried under the research project SR/S4/MS:796/12 of DST, New Delhi.

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Authors and Affiliations

  1. Department of Mathematics & Statistics, Indian Institute of Technology-Kanpur, Kanpur, 208016, India

    Kamal Jeet & D. Bahuguna

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  1. Kamal Jeet
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  2. D. Bahuguna
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Correspondence to Kamal Jeet.

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Jeet, K., Bahuguna, D. Approximate Controllability of Nonlocal Neutral Fractional Integro-Differential Equations with Finite Delay. J Dyn Control Syst 22, 485–504 (2016). https://doi.org/10.1007/s10883-015-9297-0

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  • DOI: https://doi.org/10.1007/s10883-015-9297-0

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