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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Trajectory controllability of fractional-order α ∈(1,2] systems with delay

Journal of Applied Nonlinear Dynamics 7(2) (2018) 111--122 | DOI:10.5890/JAND.2018.06.001

V. Srinivasa; N. Sukavanam

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand-247667, India

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Abstract

This paper is concerned with trajectory controllability of a class of fractional-order systems of order α ∈ (1,2] with delay in state variable and with a nonlinear control term. Firstly, the existence and uniqueness of the system is proved under suitable conditions on the nonlinear term involving state variable. Then the trajectory controllability of this class of systems is studied using Mittag-Leffler functions and Gronwall-Bellman inequality. Finally, examples are given to illustrate the proposed theory.

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