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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Controllability of Nonlinear Fractional Langevin Systems

Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 89--99 | 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, Karaikal-609 609, India

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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 Mittag-Leffler 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.


The authors are thankful to the referees for the improvements of the paper.


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