Eur. Phys. J. Plus (2018) 133: 68
https://doi.org/10.1140/epjp/i2018-11901-8

Regular Article

Numerical analysis for trajectory controllability of a coupled multi-order fractional delay differential system via the shifted Jacobi method

Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), 624 302, Tamilnadu, India

^* e-mail: pmuthukumargri@gmail.com

Received: 20 June 2017
Accepted: 23 January 2018
Published online: 22 February 2018

Abstract

This paper deals with the trajectory controllability for a class of multi-order fractional linear systems subject to a constant delay in state vector. The solution for the coupled fractional delay differential equation is established by the Mittag-Leffler function. The necessary and sufficient condition for the trajectory controllability is formulated and proved by the generalized Gronwall's inequality. The approximate trajectory for the proposed system is obtained through the shifted Jacobi operational matrix method. The numerical simulation of the approximate solution shows the theoretical results. Finally, some remarks and comments on the existing results of constrained controllability for the fractional dynamical system are also presented.