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Necessary conditions for a weak minimum in a general optimal control problem with integral equations on a variable time interval
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December 2017, 7(4): 537-562. doi: 10.3934/mcrf.2017020
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
Received July 2016 Revised January 2017 Published September 2017
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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.
Keywords: Controllability, fractional differential equations, monotone operator.
Mathematics Subject Classification: Primary: 93B05, 34A08; Secondary: 47H05.
Citation: Venkatesan Govindaraj, Raju K. George. Controllability of fractional dynamical systems: A functional analytic approach. Mathematical Control & Related Fields, 2017, 7 (4) : 537-562. doi: 10.3934/mcrf.2017020
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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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