Controllability of nonlinear fractional Langevin delay systems
Articles
Pitchaikkannu Suresh Kumar
Bharathiar University, India
Krishnan Balachandran
Bharathiar University, India
Natarajan Annapoorani
Bharathiar University, India
Published 2019-04-23
https://doi.org/10.15388/NA.2018.3.3
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Keywords

Langevin equation
controllability
fractional delay differential equations
Mittag– Leffler matrix function

How to Cite

Kumar P. S., Balachandran K. and Annapoorani N. (2019) “Controllability of nonlinear fractional Langevin delay systems”, Nonlinear Analysis: Modelling and Control, 23(3), pp. 321-340. doi: 10.15388/NA.2018.3.3.

Abstract

In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α,β ≤ 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory.

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