Controllability of fractional dynamical systems: A functional analytic approach

Venkatesan Govindaraj; Raju K. George

doi:10.3934/mcrf.2017020

Article Contents

2017, Volume 7, Issue 4: 537-562. Doi: 10.3934/mcrf.2017020

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Controllability of fractional dynamical systems: A functional analytic approach

Venkatesan Govindaraj^, and
Raju K. George

Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram-695 547, India

* Corresponding author: govindaraj.maths@gmail.com
* Corresponding author: govindaraj.maths@gmail.com

Received: July 2016

Revised: January 2017

Published: December 2017

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Abstract

In this paper, we investigate controllability of fractional dynamical systems involving monotone nonlinearities of both Lipchitzian and non-Lipchitzian types. We invoke tools of nonlinear analysis like fixed point theorem and monotone operator theory to obtain controllability results for the nonlinear system. Examples are provided to illustrate the results. Controllability results of fractional dynamical systems with monotone nonlinearity is new.

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Mathematics Subject Classification: Primary: 93B05, 34A08; Secondary: 47H05.

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Figure 1. The trajectory of the system (29) steers from the initial state $\left[\begin{array}{r}0\\ 0\end{array}\right]$ to the finial state $\left[\begin{array}{r}1\\ -1\end{array}\right]$ during the interval $[0, 1]$

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Figure 2. The steering control $u(t)$ of the system (29) during the interval $[0, 1]$

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