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Relative Controllability of Nonlinear Fractional Langevin Systems with Delays in Control

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Abstract

This paper is concerned with the relative controllability of fractional Langevin dynamical systems with both multiple delays and distributed delays in control for finite dimensional spaces. Sufficient conditions for the controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag–Leffler matrix function. Examples are provided to illustrate the theory.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, India

    P. Suresh Kumar, K. Balachandran & N. Annapoorani

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  1. P. Suresh Kumar
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  2. K. Balachandran
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  3. N. Annapoorani
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Correspondence to P. Suresh Kumar.

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Suresh Kumar, P., Balachandran, K. & Annapoorani, N. Relative Controllability of Nonlinear Fractional Langevin Systems with Delays in Control. Vietnam J. Math. 48, 67–81 (2020). https://doi.org/10.1007/s10013-019-00356-4

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  • DOI: https://doi.org/10.1007/s10013-019-00356-4

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