Kilicman, A.; Sadhasivam, V.; Deepa, M.; Nagajothi, N. Oscillatory Behavior of Three Dimensional α-Fractional Delay Differential Systems. Symmetry2018, 10, 769.
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. Symmetry2018, 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.
Computer Science and Mathematics, Applied Mathematics
Copyright:
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