Author:
Vishnukumar K. S.,Sivalingam S. M.,Ahmad Hijaz,Govindaraj V.
Abstract
AbstractIn this article, we explored the controllability of fractional dynamical systems with a single delay in the control function with the Caputo fractional derivative. It is the first work in which the author studies the controllability of a time-varying fractional dynamical system with a delay in the control function. We develop the necessary and sufficient criteria for the solution representation of controllability of time-varying fractional linear dynamical systems by utilizing the Grammian matrix. We use Schauder’s fixed point theorem to establish sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. With the help of successive approximation techniques, numerical examples validate the theoretical results.
Publisher
Springer Science and Business Media LLC
Reference54 articles.
1. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Vol. 204. Elsevier (2006)
2. Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications. Elsevier (1998)
3. Matychyn, I.: Analytical solution of linear fractional systems with variable coefficients involving Riemann–Liouville and Caputo derivatives. Symmetry 11(11), 1366 (2019)
4. Kumar, D., Singh, J., Baleanu, D.: Analysis of regularized long-wave equation associated with a new fractional operator with Mittag–Leffler type kernel. Phys. A 492, 155–167 (2018)
5. Ali, A., Islam, S., Khan, M.R., Rasheed, S., Allehiany, F.M., Baili, J., Ahmad, H.: Dynamics of a fractional order Zika virus model with mutant. Alexandria Eng. J. 61(6), 4821–4836 (2022)
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