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Approximate Controllability Results for Fractional Semilinear Integro-Differential Inclusions in Hilbert Spaces

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Abstract

In this paper, we consider a class of fractional integro-differential inclusions in Hilbert spaces. This paper deals with the approximate controllability for a class of fractional integro-differential control systems. First, we establishes a set of sufficient conditions for the approximate controllability for a class of fractional semilinear integro-differential inclusions in Hilbert spaces. We use Bohnenblust–Karlin’s fixed point theorem to prove our main result. Further, we extend the result to study the approximate controllability concept with nonlocal conditions. An example is also given to illustrate our main result.

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Authors and Affiliations

  1. Department of Mathematics, Eastern Mediterranean University, Gazimagusa T.R. North Cyprus, Mersin 10, Turkey

    N. I. Mahmudov

  2. Department of Mathematics, SRMV College of Arts and Science, Coimbatore, Tamil Nadu, 641 020, India

    R. Murugesu

  3. Department of Mathematics, KPR Institute of Engineering and Technology, Arasur, Coimbatore, Tamil Nadu, 641 407, India

    C. Ravichandran

  4. Department of Mathematics, Info Institute of Engineering, Kovilpalayam, Coimbatore, Tamil Nadu, 641 107, India

    V. Vijayakumar

Authors
  1. N. I. Mahmudov
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  2. R. Murugesu
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  3. C. Ravichandran
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  4. V. Vijayakumar
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Correspondence to N. I. Mahmudov.

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Mahmudov, N.I., Murugesu, R., Ravichandran, C. et al. Approximate Controllability Results for Fractional Semilinear Integro-Differential Inclusions in Hilbert Spaces. Results Math 71, 45–61 (2017). https://doi.org/10.1007/s00025-016-0621-0

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  • DOI: https://doi.org/10.1007/s00025-016-0621-0

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