Discontinuity, Nonlinearity, and Complexity
Controllability of Nonlinear Fractional Langevin Systems
Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 8999  DOI:10.5890/DNC.2019.03.008
P. Suresh Kumar$^{1}$, V. Govindaraj$^{2}$, K. Balachandran$^{1}$, N. Annapoorani$^{1}$
$^{1}$ Department of Mathematics, Bharathiar University, Coimbatore 641 046, India
$^{2}$ Department of Mathematics, National Institute of Technology, Puducherry, Karaikal609 609, India
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Abstract
In this paper, we first derive the solution representation of fractional Langevin differential equation represented by the fractional differential coefficient in the sense of Caputo fractional derivative in terms of MittagLeffler function. Based on this solution representation, controllability of linear fractional Langevin dynamical systems is studied by using Grammian matrix. Sufficient conditions for the controllability of the nonlinear system are established by using the Schauder’s fixed point theorem. An example is given to verify the results.
Acknowledgments
The authors are thankful to the referees for the improvements of the paper.
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