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Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems
Version 1
: Received: 18 October 2018 / Approved: 18 October 2018 / Online: 18 October 2018 (11:14:42 CEST)
A peer-reviewed article of this Preprint also exists.
Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry 2018, 10, 769. Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry 2018, 10, 769.
Abstract
In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.
Keywords
oscillation; nonlinear differential system; delay differential system; α-fractional derivative
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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